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April,

1974.

B

SEP. 1974

A PRELIMrNARY STUDY OF THE FEASIBILITY OF

AN AIR CUSHION VEHICLE SIMULATOXCHMlfJCHE r:OCE3'CIrIOot DnFT VUEc:nJIG80UWKUNDE by f(!uyverWEZJ 1 - D::::LFT

D. Band

l1rIAS

Technical Note No.

189

CN ISSN 0082-5263

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"A PRELIMINARY STUDY OF THE FEASIBILITY OF AN AIR CUSHION VEHICLE SIMULATOR"

by

D. Band

Submitted January

1974

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Acknowledgement

The author would like to gratefully acknowledge the assistance and moral support received from

Dr. L. D.

Reid, the thesis supervisor, Alan Billing, and Terry LaBrash. Without the support received from these people execution of this report would have been difficult if not impossible •

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Sumrnary

This report deals wi th a preliminary study into the feasibili ty of a simulator, specifically with reference to hovercraft. The system utilizes a HP 2l00A minicomputer and a Paceanalogue computer. Using these, the capabilities

_ of the system are explored. A hovercraft simulation with a straight road lined with simulated telephone poles is explored in detail. Design of a flexible peripheral system is executed, with regard to the specific hovercraft case.

Purposes of s imulati on are reviewed. Real time assembler and Fortran programming is outlined and is used to execute the hovercraft simulator system. One 'specific

type of control system is used, but the design is such that rapid interchange-ability of control systems is possible.

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1. 2.

3.

4.

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Tab1e of Contents INTRODUCTION

Simulators - A Conceptual Overview

1.1 General Economic Justification for Simulation 1.2 Criterion for Simulator Complexity

GENERAL TYPES OF SIMlJLATORS WITH DETAIL OF TYPE CHOSEN 2.1 2.2 203 2.4 2.5 2.6 2.7 2.8

2.9

Fixed Base and Moving Base Simulators Visual Display Systems

Controls

Choice of Simulator Type Vis ion Cues

Ins trument s Wind Effects Terrain Inputs 2.10

Detai1ed Visual Representation

Cue Treatment Yaw Pitch Roil Trans1ationa1 Modes Terrain Shudder or HUlI!P Vestibular Confusion 2.10.1 2.10.2 2.10.3 2.10.4 2010.5 2.10.6 2.10.7

2.10.8 Conditions of Reduced Visibility 2.11 2.12 2.13 Blind Simulation Control Layout Learning Carryover 2.14 2.15

The Peripheral Display Sys tem Test Equations

GENERAL CALCULATION METHOD

3.1 Equations of Motion

3.2 Equations of Mbtion Interaction with Display 3.3 General Description of Calculation Methods

INTERRUPl' CALCULATION AND DMA, MOTOR SPEED CONTROL, AND

TRIGGERING METHOD

4.1 Interrupt Calculation

4.2 DMA or Direct Memory Access

4.3 Motor Speed Control Theory of Operation 4.4 Motor Triggering Circuitry

DESCRIPTION OF OVERALL CALCULATIONS 5.1 .IOC. Subprogram Page 1 1 1 2 3 3 3 3

4

4

5

5

5

6

6

6

6

7 7 7 7 7

8

8

9

9

10 10 10 10 11 11 13 13 13 13 14 14 14

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5.2 Sample Subprogram

5.3

Out Subprogram 5.4 Pulse Subprogram

5.5

Time Subprogram 5.6 Lines Subprogram 5.7 Trsfr Subprogram 5 .8 Fan Subprogram 5.9 Plot Subprogram 5.10 FORTRAN Program 5.11 Interconnection of Programs

6.

CHARACTERISTICS OF THE PERIPHERAL DISPLAY

6.1 Basic Construction

6.2 Windowing and Projection

6.3

Distortion-Dead Area Compromise

6.4 Line Thickness ComproIhise 6.5 Unit Type 1

6.6

Unit Type 2

6.7 Noise

7 •

PROBLEMS OF THE SIMULATION

7.1 Accuracy of Peripheral Speed Control 7.2 Intermittent Nature of the Display

7.3

Programming Bug

8.

POSSIELE SIMULATOR PROJECTS

8.1 Low Speed Obstacle Avoidance

8.2 Pilot Opinion Studies for Best Control System

8.3

Night Landi~ s

8.4 Day Landings

9.

SUBJECTIVE EVALUATION OF THE SYSTEM

CONCLUSIONS

REFERENCES - BIBLIWRAPHY APPENDIX 1: Eye Visual Areas

APPENDIX 2; Schematics Al Operation of Light Sensitive Switch A2 Operation of Motor Controller

A3

Operation of Trigger Circuitry

APPENDIX

3:

Program Listings

FIGURES Page 14 14 15 15 15 15 15 15 16 16 16 ~ 16 16 17 17 17 17 17 18 18 18 19 19 19 19 19 19 19 20 21

&

22 .J.

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INTRODUCTION

In recent years, technology has produced much in the way of complex

machinery which must necessarily be controlled by a human being. Only very recently,

however, has the need been recognized for simulation of the equipment before its

construction. This is in order that facets of its operation that would prove

diffi-cult to execute by a human being would be changed before the equipment has passed

the expensive hardware fabrication stage. The equipment that is described in this thesis is designed to be sufficiently flexible that it is not limited to a single

type of craft, although the system described is that of a hovercraft. Within the

context of hovercraft, even, flexibility is an important consideration if, for

example, the effectiveness of different types of control systems is to be considered.

Recent discoveries of large deposits of oil and gas in the Canadian North have resulted in the necessity of transporting large quantities of supplie~ between distant points over ecologically fragile areas where conventional vehicles would

quickly bog down. One recently proposed method of transporting large quantities

at high speed involves the use of hovercraft over a prepared high speed pathway.

Very little research has been carried out in this area to determine if it is

feas-ible from a human factors point of view. The system chosen to be designed, then, 'was a hovercraft travelling over this hypothetical prepared pathway.

1. Simulators - A Conceptual Overview

1.1 General Economic Justification for Simulation

Simulators can be divided into two classes. These are: 1. Those for training

2. Those for research purposes

In the training case, economie justification must be derived primarily from advantages of simulation over that of actually flying the real vehicle. This may include a lower overall cost of training a new pilot as a result of a lower operating cost of the simulator and a limi ted amount of transfer of learning to

the real case, or an ability to carry out emergency procedure practice which is

difficult to execute in the real case. The latter is directed at reducing damage to the aircraft as a result of unforseen emergency situations. Cost saving is

derived from realizing that this will result in lower insurance rates for the industry

in general, and fewer suits against any particular company.

The Williams - Adelson approach (Ref. 1) weighs the cost of operating the

simulator against the saving resulting from the lower number of hours needed in the

aircraft, and the saving resulting from reduced accident rates and damage to the machine. As such, it is an extremely useful approach for evaluation of a simulator

.for training purposes.

It is apparent that hovercraft have a high operating cost per hour,higher even than most aircraft. As aresult, there is a tendency to view the criterion of lower operating cost per hour in the simulator as a very important one. Over water,

we must note that most of the procedures needed in training could be carried out on a regular.run between destination points, or at the very least carrying passengers, as there .is very little danger to the passengers in this case. Light damage to the

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are quite subject tO.disturbances. However, they do have the advantage over air-craft of having a .. relatively.low.collision .. speed with an object as a result of

.. slowing . down in the region. of. an .. obstruction . . This is .. one of the reasons that training while passenger carrying'is acceptable. If someone makes amistake, it won'tkill 100 people.

While the above may .. be. true in the case of.overwater transport, i t is emphatically not true in.the case.of high speed land.pathway transport, and

train-.. ing.in.this environment.may_be_found.to.be totally .unacceptable. There is the added

_ .. requirement in the. ground .. transport .. case. that the pilot mus t deal wi th ground slope

.. , .of a .lasting and variable.nature,_1fhereas in the.water easethe nearest to this would be a transient wave or a.port .facili ty slope. . In port the slope is antici-pated and constant, while on an.overland pathway this may not be so .

. The second criterion, th at of lessened damage through training in emergency

.. procedures., is not qui te as important in the ACV case. Wi th the present level of sophistication in the hovercraft field, there are few emergency procedures worthy of note that could not .be carried.out in the machine. Some exceptions are: fire

.procedures and plough-in. Plough-in is a situation where tuck- under of the skirt and cushion collapse causes uncontrolled rolling or pitching of the vehicle. While this is not, strictly speaking, an emergency procedure, it does represent an emergency situation, .and procedures to cope with this could be evolved.

In the case of the research simulator, we have an entirely different set of priorities. We must determine if the industry on the whole will save money as a result of the research carried out (in the case of government financed research). Thus, we must determine if changes in system operating methods would result in fewer accidents and easier control to the extent that money would on the whole be saved. Since in the case of industry, a long-term view must be taken, a relatively large sum of money.might be spent for small immediate savings, which only in the long run would become.significant .

. Studies could be carried out wi th a view to determining the best methods of training the pilot with a mlnlmum of total hours in the simulator and aircraft

weightedto take into account.the relative operating costs of.the machines.

In the present case, with the simulator designed to represent the pathway following problem, considerable saving might result from reduced damages incurred by the ACV in this high speed operation, through prior evaluation of the

effective-ness of the man-machine system, and modification of the machine portion of same .

. 1.2 .. Criterion for Simulator.Complexity

The simulator must be sufficiently close to reality that the pilot will be appropriately loaded. By this we mean that an appropriate fraction of the pilot's total available time will be taken up in flying the simulator. This should be as close as possible to the fraction taken up in flying the real aircraft. If the load-ing of the pilot is insufficient, then he may be able to carry out a task th at he would not be able to carry out in the real aircraft, defeating the purpose of the simulator.

If we find that the simulator is insufficiently complex, then we can in-crease its complexity by adding a task which takes a known amount of the pilot's time to execute.

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In order to find out if we are loading the pilot appropriately, we can use a device which loads the pilot to his limits. We measure the output from such a device (which is in bits/sec. of pilot input) and compare the two outputs, th at is, in simulator and in aircraft. This indicates the spare time available to the pilot for the two cases. Such a device is the 'bit box', where the pilot is pro-vided with an array of switches with one lit and instructions to punch the lit one as fast as he can. As soon as he punches the lit one, it goes out and another turns on. Output·. is measured directly in terms of the number of switches punched correctly in a specified time interval.

2 . . GENERAL TYPES OF SIMULATORS - DETAIL OF TYPE CHOSWN 2.1. Fixed Base and Moving Base. Simulators

For our purposes, in selecting a basic simulator type for development we can divide them into two.broad categories, that is, fixed base and moving base.

The fixed base simulator depends on cues other than motion cues from the inner ear to give the impression of flight to the pilot of the vehicle. The

'pilot's seat' quite of ten is simply a work station, consisting of merely achair and control system, with some sort of instrumentation (see Figs. 1,2). Quite of ten this works weIl enough for all but the most advanced simulators.

Moving base simulators vary widely in complexity, from one or two degree of freedom types to the most bulky, the six degree of freedom monsters such as the lunar lander simulator. This type tends to be quite expensive because of the added

.cost of the serve systems needed to effect the motion of the simulator and the added space in some cases needed to house the simulators. While it would seem on the surface that much is to be gained through the use of motion in the simulation, it has been noted in the past that such motion produces doubtful advantages. The motion simply introduces more motivation into the simulation, something that the more experienced pilots already have (Ref. 1).

2.2 Visual Display Systems

Display systems on these simulators can be of several types. They include a three dimensional display such as in the real world (i.e., a window to look out), a Itdistantlt two dimensional display in which the display takes the form of a

pro-jection onto a screen external to the cockpit of the simulator, a pseudo-distant display in which a close two dimensional display is given simulated depth through the use of a collimating lens, and a close two dimensional display which generally takes the form of a cathode ray tube.

By far the most common type is a fifth type which neglects external cues

.entirely and simply provides the pilot with instruments for determining his attitude. Quite of ten, for motivational purposes one finds secondary cues in the simulators,

.such as wind noise or engine noise. 2.3 Controls

Controls in a simulator are generally duplicates of those in the aircraft that they represent. Active force feedback, however, is present in only the more advanced.simulators. Active force feedback controls are the type where the force gradient and the zero position of the control actuator change with the condition of the vehicle simulator in flight. Thus, the force gradient becomes higher with

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higher speeds for an aerodynamic control, as the aerodynamic forces vary as the s~uare

of the speed. The primary reason forthe absence of·this feature is the high. cost.

Some simulators provide no:active force feedback, while others try to simulate

feedback at a cons tant· speed by adding return springs to the actuator. Control force

gradients were neglected in our initial simulation.

It should again be noted that there are two purposes for having a simulator,

and these are research and training. In the training mode, it is ~uite important to

safeguard the motivation of the student, in order that he will learn faster. Force

gradients on the control'actuator also play a role in the training case in

develop-ing a "feel" for the aircraft. In the research mode, it is ~uite of ten found un-necessary to go for realism in the extreme because of the greater experience as a

whole of the persons using the equipment. In this case, it is assumed that they

have some idea of the "feel" of the aircraft before they climb into the simulator.

These people are in general already motivated and thus the absence of some cues

makes little difference to them, as they tend to concentrate on the task at hand.

2.4 'Choice of a Simulator Type

In choosing a simulator type, one must take into account the economie .reality, the conditions under Which the simulator will be used, the space

limita-tions, and the calibre of personnel that will be using the equipment.

The present system is primarily a research simulator. It must be made

flexible to accomodate a large range of simulation. Space and budget limitations

make.a three dimensional display and moving base simulator impractical. A distant

two dimensional display method, because of the space heeded, is also out of the

question. An instrument only display is of little use for primarily visual contact

piloting such as is found in the operation of a hovercraft. Contact flying is the

type of flying where the pilot is constantly referring to cues from a realor

re-presented outside world. Instrument flying is the type of flying where he attempts

to reconstruct the vehicle's attitude through the use of vehicle instruments. Limitations imposed by the above resulted in the choice of a close two

dimensional display on a fixed base simulator, with the option of changing this to

a 'pseudo distant' display through the use of a collimating window.

2.5 Vision Cues

It would seem apparent that in the case of variable terrain, the pilot

gains a preview of the terrain in looking out the window of the vehicle. He has

an idea of the terrain that he is going to cross and a definite idea of how long

it will be before he crosses that terrain as a re sult of his depth perception.

The .distant depth perception needed is obtained through comparison of the apparent

size of known objects with their real size. It is imperative, therefore, that some

depth pereeption be maintained, whether produced from faithful reproduction of .surrounding features, or through a three dimensional display. Large areas of

un-broken snow in the North are common, and the absence of visual cues in this case

.make unaided landing difficult if not impossible. The standard solution to this

problem is to cut trees and stand them up beside the runway. These alone are

sufficient to provide the pilot with the depth cues needed to make a successful

touchdown .

. Speed information is obtained partly through use of the peripheral V1S1on

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occurs when the objects become blurred to the eye through their movement through the field of vision. The angle of 'movement and the ex tent of the streamering provide important speed information to the pilot on final approach (Ref. 2). When using a.computer simulated display the terrain preview mentioned apove, while quite useful, may take so much computer time to display that it becomes impractical when the display itself is complex. Since .the display complexity determines the amount .of computer time used and thus the amount remaining for such things as preview, one

may find that there is simply insufficient time for such an undertaking. 2.6 Instruments

Instruments, while admittedly an aid to centrol of the machine, are not likely to .be a major factor in determining the control of the vehicle in a high speed contact type tracking'case, because of the time involved in fixating on the instruments. If some instrument .was provided that gave the pilot a good idea

of .his position with respect to the sidesof the track, instrument control would be

maintained, although the pilot would lose the preview obtainable through looking

.. eut . the .wind.ow. I t is probable, therefore, that he would go back to the visual .. display and leave the instrument if the display gave that preview. Note that in

this case we are·talking of all types of preview, and not just terrain preview. The mere addition of known objects in the display gives some velocity and depth information which is a form of preview.

2.7 .Wind Effects

.Wind has a large effect on the dynamics of a hovercraft. A gust can tilt the vehicle, with the result that there is a sideforce provided by the air cushion which adds to the sideforce provided by the wind. Yaw is also generated as a re-sult of the frequent presence of a large stabilizing vertical fin on the vehicle. Because of this, the pilot tends to be quite interested in any information on wind direction and strength that he can garner from the display. This is particularly true in the case of strong winds.on a pathway. The vehicle is intermittently shielded from these winds by trees or other objects beside the pathway. At water based hovercraft terminals one of ten finds windsocks or other wind direction and

.strength indicators, whichaid the pilot in judging the conditions that he is going .to encounter in docking.

Information pertaining to wind can readily be added in almest any visual

.display through the use of a line of varying slope and length, indicating direction and strength. In order to evaluate the effect of this knowledge on a pilot's per-formance, it is expected that this will be studied using the simulator for the pathway following case.

2.8 .. Terrain Input

Terrain, as mentioned earlier, also has a large effect on the dynamics of .. thehovercraft. Camber of the surface makes maintaining a straight track much .more difficult if the camber is such that there is a crown or high spot in the

centre of the path. This is common practice for better road drainage on most high-ways. The reverse effect is also true, in th at a camber resulting in a low spot provides a centering force on the vehicle through the tilting of the lift vector of the vehicle. This lowers the work load on the pilot considerably.

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on the pilot as well, since he must provide for sidethruston the vehicle to maintain the track of the vehicle within specified limits.

2.9 Detailed Visual Representation

Unlike aircraft simulation, where most manoeuvers are far from objects

(except for landing), hovercraft are.constantly manoeuvering near obstacles in an unconventional control situation. Simulation under theseconditions is naturally disposed toward contact simulation, as most flying of the vehicle is done looking out the window. Instruments in themselves are seldom satisfactory for this sort of flying. The Norden Contact Analogue Display (Fig. 9) is an attempt to' provide the pilot.of an airplane with a representation of the world outside. This consists of a monotone 'sky' and.a checkerboard flat earth, with a vanishing point for the

squares of the checkerboard at a horizon. This particular analogue is unsuitable for hovercraft,however, as translational motion is ignored here, whereas in a hovercraft, translational cues provide much of the pilot's input .

. .. . It is apparent that we must, for the purpose of research, simulate

.. . reasonably .fai thfully the reaL environment, subject only to financial constraints . Thisis .asimulation where we are not familiar with which cues are important, and

thus .we would like to provide as many as possible.

Some sort of model: of the situation could be built, if we were to follow the above criterion. This model could conceivably be built in.three dimensions, .and .then a closed circuit television used to view the model, but this method is .qu~te ccstly and relatively inflexible. The method finally adopted was to reduce

the cues .tc the basics, that is, to the side of the road, a telephone pole re-presentation, and the horizon, along with the centerline of the path. This model was then drawn in perspective using the computer. The number of poles was limited

in order that a reasonable amount of memory and time was used to draw the picture.

Peripheral V1Slon was catered to by using a 'pole projector' for the side window (see Figs. 10,11).

2.10 Cue Treatment

For the purposes of the simulation, we must determine same preliminary

idea'ofthe importance of the various cues available to the pilot. The motions treated here are roughly representative of the Bell SK-5, type ACV.

2.10.1 Yaw

Yaw angles tend to be large for hovercraft. Where a high speed turn is

negotiated yaw angles can be as large as forty degrees. Strong side winds can

.also induce large angles of yaw, particularly "at low speeds. An attempt to main-tain track.along a steep.slope (for hovercraft) of ten degrees will also result

in large yaw angles. In order to simplify the calculations involved in the display,

it was found necessary to limit the yaw angle to about ten degrees. This is not an unreasonable value over a _ prepared path, since at high speeds 'sidewinds can be

.successfully bucked at small. angles, there are no steep sideslopes, and on a straight

road there is no attempt at high speed tight turns . . 2.10.2 Pitch

Pitch angles are relatively small in most types except during plough-in or other extreme manoeuvers. There is the conceivable situation, however, where the

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craft can climb a hill. Thus, it was considered a good idea to program this in. a small engle approximation, end.limit it to ten degrees. It was left as a latent capability, however, in this_simulation. A normal maximum for hovercraft is about

o 2-3 .

2,10.3 Roll

Roll angles are somewhat larger than pitch angles, although still small

in.hovercraft. Roll is primarily induced through centrifugal force in a turn, or sideforee, and as such are unlikely to be significant .in a straight line tracking simulation. The capability should be considered, however, for other forms of simu-lation. The road display may prove impractical, however, as the advent of tilted poles on .the screen slows the computation down. We do not have roll capability

in the version outlined here, but if the capability is desired, it is a simple .addition to the main program. Roll angles are of the order of 30 •

2.10.4 Translational Modes

.Translational modes should for the most part be simulated as this necessarily involves a. change in perspective of the poles. Hump, or up-and-down .movement of the vehicle, can be neglected, as we have a prepared surface. A.latent .capability was programmed,.however, as in the case of pitch, in order

that ready.adaptation to other.forms .of simulation can be achieved . . . 2.10.5 . Terrain Input

This can be stored on digital tape. The track number could correspond to lateral position on the path, and the tape location to the location along the leng th of the path. In this way.a representative path can be flown.

The problem of preview of terrain and route with a contact analogue dis-play. i's . a nontri vial one. If we view an imaginary working display wi th the property of providing proper preview, then we have something similar to that in Fig. 12. Note, with.a turn coming, there is a very complex curve in the road.

In the real case, surface roughness of the road is also included. A pre-liminary study of this system was carried out on an IBM lBO, but simplified to the extent that roughness and 'one shot' obstacles were neglected. The program execution time corrected for use on the HP 2100 was too long for effective realtime calculation. Output from the program is shown in Figs. 10,11.

2 .10

.6

Shudder

Shudder of the vehicle in a hump mode can be an important limiting factor

.in the :case of travel at high speed over rough terrain. The physiological limits of the pilot may prove to be the limiting factor in this case. The simulation in our case, is, however, limited to a prepared path .

.. 2.10.7 Vestibular Confusion

The vestibular system in the inner ear " provides the human wi th his sense of balance. A confliêt between this system and what the eye sees results in

many. of the problems that pla.,gue simulators. In a fixed base simulator, for example, the.vestibular system indicates to the pilot that he is not moving at all, while

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contradiction between VlSlon and the vestibular system is quite common, and is

resolved in favour of the visual system. This is because the vestibular system

is subject.to many errors when .the stimulus is constant.or changing slowly, because the system is based primarilyon accelerati6ns. Vision is not.Again, the system was designed by nature to function primarily on a two dimensional plane, .which makes it unsuitablefor three dimensional flight .

. In the case of a simulator, the confusion produced by these contradictory

.stimuli must be resolved in favour.of the stimulus the simulator is attempting to create if the simulationis to be effective. If the stimulus in a fixed base simulatorallows the pilot to visually reference himself to the cockpit, then

.there is no confusion and the pilot quite happily decides that he is sitting in a

.. stationary chair. If we provide no cues indicating that the pilot is stationary from. the .. work station but only those indicating motion . fr om the simulated outside world, then it becomes very easy for the pilot to feel as if he is actually in

the·moving vehicle rather than·the fixed simulator. The further the simulator is

from.the ideal, the more difficult it is to convince the pilot that he is 'flying' the·. vehicle '. and the more difficul t i t is for the pilot to convince himself.

The size of the simulator-produced cues versus the size of the cockpit .cues is.one of the determining factors in this battle of the senses. The pilot's

belief in the simulated view increases with size. If the display is good enough and the pilot has managed to convince himself that he is flying the vehicle, then the effects are qui te spe.ctacular. Pilots have been known to fly the vehicle as

if their lives depended onit, then break into cold sweats when they 'crash'.

Our peripheral display is designed to provde this larger, more convincing

.effect. It should not be confused with the command or 'head up' type of peripheral displaywhere the pilot isgiven a command through the use of his peripheral vision. Our systemprovides no command information, and as such is not sub~ect to many of the constraints for effective control .

. . 2.10.8 .. Conditions of Reduced.Visibility

Recent tests in Northern Canada have indicated_that large amounts of dust are kicked.up by the blast of.air from the hovercraft cushion, when operating over tundra • . This brings up. the .possibili ty .of operatin~ _ the vehicle in reduced visi-.. . bility, and .. thus simulating this . .. Fog .. is a different. type of' problem from that of

dust . .. In fog, different.objects disappear into the fogfirst. This makes it rela-tively difficult to simulate. With the local dust cloud, there is a more or less general reduction in acuity both for near and far objects. This particular type of problem can be simulated on the display if the display is on a dual beam oscillo-scope. One beam of the display can be used to provide the pilot wi th his perspec-tive.view of the outside world, while the other provides the dust. This is

accomplished using the following method: the CRT is scanned using standard tele-vision type circuitry, while the "z".or brightness aXis is modulated with a noise generator .

. . Fog can be simulated. at the moment only through the use of the computer,

.since more .distant objects.must disappear. This takes much computer time, and

. thus is limi ted to expensive .. equipment .

.. _ .... 2.11. Blind.Simulation

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fundamentally different .. types .of simulation. Theseare"first, the blind simulation, and second; -the known simulation. The blind simulation~.involves the simulation of a situation in which no one has found himself to date,.in order to evaluate the per-formance, of . a particular man .... machine .. configuration. -.: The· known simulation involves simulation of a situation in which the simulator and pilot perform manoeuvers in a knownand .. well-documented: environment.

Differentiation.between the two· types is necessary because in the known situation, the precise.cues'necessary for adequate man-machine performance are well known, and:well documented. This'makes it relatively easy to set limits on the cues· that . are included -in: the· simulation, because the· consequences of leaving the cues out are known~ In the case of the blind simulation, very little is known, and.thus·every effort must be'made to keep the maximum number of cues available to the,pilot. When this hasbeen researched and compared to the actual situation,

.. some of. the cues can be· removed,· and this becomes a known si tuation. This simu-lator is .in the transition stage. Simulators of hovercraft have been built, and hovercraft flown, but little is known of the cues necessary in the pathway follow-ing case with a hovercraft simulator at this point.

·.2.12 Control Layout

The controls in the simulator are arranged such that the entire instrument panel can be removed in_about thirty seconds. This facilitates changing the mode of the simulator from one requlrlng one type of instrument set to a type involving an entirely different set. To some extent, as well, controls can be changed with the instrument p.anel. Control types wi thin the context of hovercraft control can be exploredwith relative freedom, allowing~o~.research into the effectiveness of various types of systems. Figure 13 indicates the quick-change mechanism.

Basic System

The basic system consists of an aircraft style yoke, rudder bar, and throttle.The yoke controls sideforce through rotation. Propeller pitch control through push-püll motion. of.the yoke is under consideration. The rudder bar controls yaw of the vehicle, and the throttle at this point controls fore and aft thrust. In the SRN 3 (see Fig. 14), sideforce is obtained by rotating the pylons carrying the propellèrs. Yaw is obtained through use of the rudder and through differential rotation of the pylons. Finally, fore and aft thrust is obtained through modifica-tion of propeller pitch.

,On the simulator, the function of the controls is readily modif-iable since this involves only programming changes on the analogue computer.

2.13 .. Learning Carryover

Learning carryover is a term used to describe the fact that aft er a pilot has flown a simulator for a while he will tend to carry some of this training with him to the real aircaft. The extent to which this occurs depends on what he is asked to do.For example, if, in the simulator, he is asked to push on the stick to in-crease.speed, and in the real craft the opposite occurs, he will experience negative carryover of experience when he tries to fly the real craft. That is, he will tend to attempt to increase his speed by pushing the stick. Similarly, if the stick is hooked up· the same way in both, he will experience positive carryover. An inter-action diagram illustrating this effect is shown in Fig. 15. Nuances of the effect

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they may have different hand grips. 2.14 The Peripheral Display System

A peripheral display system is a system which isdesigned to operate outside the visual field of the fovea. The fovea is the most visually acute part of the eye, and is the part_that is used for examining things in detail. When you look. at something, the'fovea is automatically centered on the most interesting

spot .(see Appendix 1.).

Methods ofproducing. the desired peripheral motion cues are quite varied. One of them is a rotating disc which is masked to provide a vanishing point and the appearance of a field beside the observer. (see Fig. 16). Others involve

rippling lights,moir~ patterns, CRT displaysand modeis. For our purposes, we chose telephone poles in the main display~ so these were chosen for use in the peripheral display as weIl. Model poles were immediately rejected as too expensive and in-flexible. CRT's were too expensive. Thus, we arrived at a simple projection system which projects a vertical white line on a frosted screen. The line moves as the pole would (see Fig. 17).

The drive mechanism for the dislay must be carefully chosen. This mechanism cannot be aservo utilizing potentiometer feedback as this would soon exeeed its normal travel and become useless. It is logical to expect, therefore, that instead of the position controlled mechanis~, we will have a rate controlled

type'. . This will set the speed of traverse of the pole to a speed gi ven by the computer, with the beginning of the traverse triggered by the computer .

. It was decided at this point that it would be fruitful to design a system

utilizing a small geared DC motor with speed control to run the system. Counter EMF feedback could be used to control the rate of rotation of the motor armature, and the DC motor would-allow direction reversals without undue difficulties. As a re sult , the circuitry in Appendix 2 was developed. Because of the nonlinearities of the system, an inverse transformation obtained from the speed calibration curve

was added to the fortran program controlling the output speed in order that the

system would perform as required. 2.15 Test Equations

In order to get an idea of what was involved in the calculations, it was decided to initially model an ACV in a low speed configuration, that is, puff port

in yaw, thrust, and sidethrust. Puff ports are essentially controllable openings

into the cushion used to provide pure thrust. When one is open, it vents cushion air outwards in a stream, and the reaction provides the thrust.

The use of these basic equations was deemed sufficient to test the system in the early stages. In order to be able to model the equations of motion of the vehicle sufficiently weIl in other than a test situation such as this, it would be necessary to increase the sophistication somewhat. Approximate transfer functions of nonlinear force characteristics can be calculated for most degrees of freedom, and programmed into theanalogue computer using a segment generator.

3 . GENERAL CALCULATION METHOD 3.1 Equations of Motion

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, . . . - - -

-this case. Yaw, side motion and.forward motion were coupled second order equations. No concerted: attenu:>t was made. to . make .. these equations conform to a particular ACV.

Figure 18 shows the equations as programmed. 3~2 .Equations of Motion Interaction with Display

From Ref. 3, we have the following approximate maximum values: longitudinal u

=

1/10 g.

lateral v

=

1/20 g.

hump smooth surface - neglected. yaw accln.

=.6

rad/sec2

Roll

& pitch

.acceleration are neglected. Rollof the order of 2_30 (Ref.

4)

Pitch of the order of 2_30 (Ref.

4)

While most of these exceed the human threshold levels, we have, as previously outlined, a way to simplify the situation. If the display is made

sufficiently large and convincing, then the pilot will reject the vestibular input. Thus we rely on visual cues to provide the sensation of accelerations and movements that exceed the threshold. The solution.to the problem in simulation

.. here, then is the use of.a .normal fixed base simulation with a visual display th at hopefully can provide the feeling of ~otion that we require for the simulation. We mustnote,however, that it is not only the simulation display, but the attitude

of the'pilot as well that .determines if this can be achieved.

For perturbation type manoeuvers, the nonlinearities associated with

.large .. angles can largely. be neglected, and thus this vastly simplifies the analogue

.. portion.of.the simulation.

The only truly large input to the pilot in the vehicle is yaw accelera~ion. A value.of

.6

rad/sec 2 is cited, compared to the threshold of approx . . 1 rad/sec . This.would occur· if the vehicle for some reason was found at a 900 angle to the air-flow at high speed. Considering the.small angle approximations to the motion of the vehicle· in the close high speed tracking case, this is highly unlikely.

3.3 General Description: of,.Calculation Methods

In this simulation, there are four major areas of concern with the digital computer.calculation for the display. The first is projection, or the method used to locate a point on the screen from the imagined outside world. This constitutes the backbone of the calculation, and time lost here is a large proportion of the total calculation time . . · Iwill consider only the straight road case. Here, if we take the general nonlinear version of.the outside world, and then transform it with a matrix.consisting of sines and cosines, etc., the display may not be fast enough,

. because these functions take a large amount of central processor time. We opt,

therefore, for a simplified version. Pitch and yaw of the vehicle utilize small

'angle approximations, whereas translational information is used precisely to project the points on the screen exactly as they would appear in perspective. This is

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we can construct a series_of similar triangles from the location coordinates of the

.point _in question~ Thus.,_ if .. the .distance from the observer is Z along a reference axis, the _height above a plane _paralleL to the ground and through the observer 's eye is Y, and the distance from the Z axis is X, we have

X

=

s y

=

s XD Z

YD

Z

where the subscript 's' refers to the fact that this is the corresponding coordinate on the screen.

Because of the large amount of

epu

time that is used in creating this per-spective view, it was decided to utilize the computational ability of the Pace TR-48 analogue computer to reduce the load on the digital machine by solving the equations of motion. Sampling of.the output· of this machine was done each time the perspec-tive view was changed. This occurred on'therorder of three times a second. Rapidly changing inputs would not be detected by the sampling device in this case, and thus the output to the digital computer was limited to position and velocity. This re-sulted in at least first order smoothing of the control signal before it reached this sampling network .

. When the display is changed,. it is considered to have been "updated". When it .is unchanged, that is merely replötted to keep it bright, it is said to have been .Ilre freshed". Nothing at all changes when the display is refreshed, while

.updating.provides new information from the computer for display, even though, for example, .the perspective.position indicated on the screen doesn't necessarily change.

- _ .The refresh rate on the HP 2100 is controlled by a resistor-capacitor

.ti~iàg :network. It is shipped set for refresh every twenty milliseconds. This was considered too of ten, and.was modified to once every forty milliseconds. There re-mains .the possibility of slowing it still more, to ab out once every hundred milli-seconds or ten per second. Flicker in this case would be the limiting factor. The reason that lengthening is necessary is that every time the view is plotted, it takes up a large amount of computer time, which could well be used elsewhere.

Windowing is the third of the problems and a very important one. If the

. system is allowed to calculate the location of points which would not nói'maIly'fall on the projection screen, two things happen: excessive time is spent on unnecessary

.caleulations, and when the _points are plotted, they take the form of folded or re-versedimages, as indicated in Fig. 19.

The standard method for handling this sort of problem is with "if" state-ments in which, if the point happens to fall beyond the borders of the display, plotting.and further calculation_is inhibited. In the case of lines which extend

.beyond the edge of the screen the slope of the line must be maintained to the edge.

This .is done by calculating where the line would intersect the edge, and then joining that point with the point in the viewing area of the screen .

. Triggering of.the peripheral display system is the fourth problem. It involves two variables, the velocity of the traverse and the time th at the display begins to traverse.

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....

. . .

...

'

The peripheral display approximates a window on the side of the vehicle. This"window" was incorporated'into the calculation of the equat"fons of velocity for the displayed line : moving across the screen and the time' at which the display should start its traverse. The time that the traverse starts was approximated by the time.that the "poIe" passed·the si de of the vehicle, or a point slightly dis-placed from this, with a slight correction for yaw. Differentiation between forward and reverse traverses iS'accomplished-by shifting this zero. In order to calculate where·thepoles were,a-zero point~was established and the poles were assumed to be at'8,'_uniform spacing from this fixed'zero point·~- 'Then, knowing the location of the.vehicle.with respect to this zero, it is a simple matter to calculate the loca-tion of the poles on the-' screen .

.

4

•.

INTERRUPT CALCULATION~AND_DIRECT MEMORY ACCESS, MOTOR SPEED CONTROL, AND .TRIGGERING METHOD

'. ~ .. l . Interrupt Calculation

. Interrupt signals are internal signals in the digital computer which allow computer.programs to interrupteach.other, much the same as people interrupting others .in conversation. This allows for rapid execution of many programs almost simultaneously. In the system under development, for example, there is a Fortran program vhich is constantly calculating new perspective information. If the time base generator provides an interrupt signal, which it does every ten milliseconds in this case, the computer stops executing the Fortran and begins executing a time base generator program. 'When this is through, it returns to the Fortran program and continues on as if nothing had happened. The advantage to this method is that programs which would normally spend'a lot of time in waiting lqops, waiting for outside devices to catch up, are'serviced when needed and ignored at other times. There is a set of pribrities set by the type of hardware that is requesting the interrupt. This determines what ean interrupt what. This is illustrated in the digital computer organization diagram, Fig. 20. This is to prevent a slow program .from stopping an extremely fast one.

~4.2.·Direct Memory Access

This system allows the user to bypass the processing regls~ers in an out-put sequence. Generally, in order to outout-put a value to a peripheral device, the value must be first accessed from care, then loaded into the A and B registers. From there, it is loaded into the output register on the particular output card in question. This is quite time consuming when a large block of data is to be transferred. In order to.get around this, direct memory,access takes a block of data from_core and outputs it directly to the output card. This is done while the computer operation is temporarily suspended (once for each memory location). The.system operates independently from the rest of the computer .

.

4.3

.Motor.Speed Control.Theory_of Operation (see Appendix 2)

. The peripheral display motor speed control is based on the principle that a DC.motor also acts as a generator. The motor generates a voltage while the armature .is.turning which,is in opposition to the current flow. The magnitude of this

volt-age varies roughly as the speed of the armature. Thus, if the total voltvolt-age across the armature is V, the current through the armature is I and the resistance of the .armature.is R, we have the approximate relation:

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C.E.M.F.

=

v -

I*R

The resistance of the armature; in this .case refers to the ohmic resistance of the armature and brushes.C.E.M.F. is the generated or counter electromotive

force. . The relation is approximate as we are neglecting such terms as inductance,

.capacitance, and distortion of.magneticfield of the motor due to the current

flow-ing through the armature~ The voltage obtained from a difference amplifier with

.inputs the applied voltage·and.the current can thus be used as a tachometer input.

The voltage is fed to a'comparing amplifier which compares it with a reference voltage. This reference'voltage comes from the digital computer, and thus controls the speed of the motor.

4~4 .Motor.Trigger Circuitry

The trigger'circuitry must have the following capabilities: to begin a scan, the computer must.be able to feed in a start signal. The speed voltage from the computer must be relatively .unattenuated by the time it reaches the motor controller. A stop trigger must be provided at the end of the scan.

The criteriawere met by the following method: a start signal from a singlechannel of the D/A converter was coded into positive and negative signals to separate the two channels (left and right displays). This was fed into a diode and .inverter network so th at one of two flip-flops would receive a signal to "flip". The one that received this signal would be the flip-flop correspond-ing to the display that was to start. A flip-flop is a bistable device, which can output either a logical "1" or a logical "0", depending on an input signal. Once set, i t is stable until reset. . Wi th this flipflop "flipped" an output relay is driven, .which connects the .speed voltage from the computer to the motor speed controller. The motor then turns. When the displayed pole passes over a light sensitive switch, it triggers it to "flop" the flip-flop, de-energizing the relay and connecting the input of the motor controller to ground. This stops the motor. The circuitry is illustrated in Fig •. 24. The filter in the figure, is designed to

.remove.noise so that the .system.will not be triggered to stop inadvertently.

5

.

DESCRIPTION OF OVERALL CALCULATIONS (See Appendix 3) · . 5.1 .. . IOC. Subprogram

.This program comes as a part of the HP software. It is designed so that a call to it will input or output information through a peripheral device. The name stands for "Input-Output Control" . . While useful for short output sequences, because of.its complexity it tends to be slow for very fast or very long ones .

. , ... 5.2 .. Sample Subprogram

.This program. uses ... IOC •. to sample eight channels of analogue input con-verted .. to . digital in the AID Converter Sample rate is approximately lOOk samples/ sec. when it is sampling. This occurs once per update.

· '. 5 .3 .. Out . Subprogram

This program uses.IOC. to output through the high speed Digital-Analogue

.. . Converters .the desired speed of.the peripheral display motors. This speed is changed once per.update. In between, because.the D/A converters have separate registers, · the.value.remains constant.

(21)

.

5.4

Pulse Subprogram .

This program outputs a.start voltage through the Multiprogrammer using

.. IOC. to the motor trigger. The voltage outputted depends on the input of the program 1,0, or -1. Through theuse of the Fortran program, the voltage is

re-. turned. to zero very shortly thereafter; in order that no' contradiction occurs be-tween the.start voltage~and·the stop voltage supplied by the light sensitive switch .

. 5,~ 5 ' . Time, Subprogram

This program af ter being started, interrupts every ten milliseconds what-ever.program is in progress and.increments its output variabie by one. When it is called again, it sets the .output·variable to zero andonce again begins counting.

,Thus,it.gives a measure of ,how .. long the interval is between calis. It cannot interrupt.when the interrupt system is shut off, however, as occurs from time to time during execution of the program, and for that reason some errors, although small, will be present .

.

,

5.6

.

,Lines Subprogram

This program is designed to interpolate between two points given by the main program, digitize .this .information in terms of the intermediate points, and

store the.information in'a working area in core. It returns to the program the lastlocation used, provided~it is .given a starting location. Special cases of vertical.and horizontal'linesare taken into account for greater speed .

. 5 ~ 7' •. Transfer Subprogram

This program shifts all points from one area in core to another af ter one perspective view has beencompleted. The initial location is the working area in core, the final location.is the output location in core. Use of the separate reg-isters prevents half-completed'pictures from being plotted. The program also sets

.thestarting location of'both buffers and provides that information to the Fortran program:when initiated foruse:in other subprograms .

.

5.8

'

:Fan. Subprogram

This program provides the Fortran' necessary to divide the path into equal sections and provides centerlines and.edges for the road.

5

.

9

Plot,Subprogram

This program provides .forthe high speed output of the contents of the output memory locations~provided .by· transfer through the use of the dual

8

bit DIA converter. This converter is specifically designed to interface with an oscilloscope and provides its.own blanking pulse to illuminate the' plotted dot. Direct.memory access is used in the high speed version of this program to increase .output speed. It is not possible to interpolate between points using the

DIA

con-, ,.verter simply by neglecting the blanking pulse. This is because of the nature of the method of loading new information into the registers of the device. An etch-a .sketch type of path would be traced out between the initial and final points with nothing.certain as to location in between. In order to accompllsh this interpolation

,a .vector generator is required. At the speed necessary, this type of device is prohibitively expensive.

(22)

The dual

8

.

bit hardware interrupts once every forty milliseconds in order to keep the display illuminated.

5.10 Fortran Program

This program is quite flexible and readily programmed. It contains the

information for the perspective calculations and can be adapted to different types

of simulation. Persons relatively unskilled in the vagaries of HP. assembler can

readily program the system for their display since they can program the master,

pro-gram in Fortran. The Fortran master, while not extremely fast, makes up for this

through its flexibility.

5.11 Interconnection of Prog~~ (See Fig. 25)

The system consists of a loop with the start and end points at the pilot's station. The start point is the pilot's actions in moving the controls. These con-trols are connected to the analogue computer. Processing in the analogue computer

results in position or velocity information in the various degrees of freedom of the

simulator. This is fed to the analogue to digital converter, which converts it to a

form which the digital computer can use at a rate which is close to its maximum

capability. This information is processed by the digital system in two ways. One

involves .the high speed 8 bit digital to analogue converter. This simply outputs the dot position information (corresponding to the perspective image of the imagined

world) onto.the screen. The second way determines the peripheral velocity and trigger

information, and outputs this to the control system through the 16 bit high speed

digital to analogue converter. In this section, high speed is not critical. Wherever

possible arithmetic is done in integer arithmetic as it is faster. Floating point

arithmetic is the only solution in many areas, however. For an interconnection

diagram, see Fig. 26.

6. CHARACTERISTICS OF THE PERIPHERAL DISPLAY

6.1 Basic Construction

The peripheral display uses a rotating cylinder which is opaque except for two vertical clear bars. The cylinder is illuminated by a vertical filament bulb. This bulb is placed in the centre of the cylinder. The resulting vertical line is projected on a frosted pane of plexiglas. We thus have a primitive projector. Using a line light souree instead of a point souree decreases the sharpness of the

projected image somewhat since the filament is not precisely straight, but the image

is much brighter. The velocity of the projected line depends on the angular position

of the cylinder, the rate of rotation of the cylinder, and the distance from the

.cylinder to the projection screen. See Fig. 27 . We use as our ideal a constant motion

ofthe projected pole for the parallel displays, as a real pole would move in this

.manner .. The distanee from.the filament to the cylinder is fixed. Note the difference

.from the ideal linear case and the actual case is small for smallQC .

. 6.2.·Windowing and Projection

While windowing is taken care of by our trigger circuit, projection is still

aproblem. The calculation technique is similar to the central display for a display

parallel to the side of the pilot's head. This becomes complex for displays at an

angle, but a simpler technique can be used as indicated in Fig. 28. We find that the

(23)

X'

-x

Gamma)

where X' is the distance of the pole from the observer parallel to the road, X is the distance from the edge of theroad, Wd is the perpendiculardistance from the

,pilot's eye of the display, and Gamma is the angle -that the-display makes with the side'of the pilot's head. X is the screen location of the pole. Note for

s

y

=

0 X , s

=

Wd X '/X. Thi s is the linear case. 6.3 'Distortion-Dead Area Compromise

Accuracy of the speed of the pole on the parallel displ~ is best when the ,cylinder is far from the screen,as the angular movement of the cylinder is less (see Fig. 27). This, however, results in a very large "dead" area which the system has to traverse before it comes to a stop af ter triggering the light sensi-tive switch. If it is stopped just af ter the traverse leaves the screen, then there is adelay ',when the system is, triggered while the cylinder traverses to a point where a 'new pole is projected. If the ,cylinder is allowedto traverse just short of projecting the next pole before it is stopped, then if 'the cylinder reverses direction, that is if the,hovercraft reverses its direction of travel, then the

-same delay-occurs. Three cases, too close, too far, and satisfactory are shown in Fig. 29.

,6)+ '::tine ,Thickness ...compromise

The width of the projected line is another factor which must be reached by a .compromise. If the line is allowed to become too wide, it becomes a projected light area to the pilot instead of,the desired pole. If it is too narrow, then the system will be unable to bring the cylinder to a halt with the light sensitive switch illuminated'by the projected line .. This is necessary to allow rapid direction rever-sals, asindicated in Fig. 30. A certain amount of elasticity in the system, coupled with the smoothing capacitor in the motor speed control circuitry results in a small

amount of 'bounce' in the ,system when it comes to a halt. With a narrow pole and high

,speed this results in the projection bouncing back to the previous position with respect-to-the light ,sensitive switch. Thus, in order to restart, it would be necessary to provide two start pulses.

6~5 linit Type #1

A "Type #1" unit consists of a display designed for use parallel to the side of the .head. This system neglects the errors inherent in its speed and simply approxi -mates a constant velocity throughout its traverse. The errors in the velocity are out

-'lined on Fig.27.

,6;6, ,Vni t Type #2

A "Type #2" unit consists of roughly one half of a type one unit at an angle to'the pilot's head. In this case, with a proper .choice of angle,. distance from the pilot's head, and cylinder location, the nonlinearities associated with the display are taken into account, and used to approximate the nonlinearities associated with

placing~the display at an angle.

,We have two functions tnvolving X. They are the desired function

X

=

f('r ,X'), and the actual function,' X'

=

sf(oc.) as shown in ,Fig. 18. In the present

(24)

design the display motor rotates at a constant rpm. Thus, we try 0(= K1XI + K

2 where Kl and K2 are constants. The actual function becomes: X~ =f(K1XI + K2). Now, juggling Kl' K2' and Ywe curve fit for minimum difference between- -Xs s--and-X' -over a range · of··CX:~ - The . curves are shown in

-Fig. 31. In this case,Ki = 2o/foot,-and K

2 is _73

0

. The result is a reasonable

fit, as shown. The problem, however, is that this must be restricted to yaw angles near zero or-the accuracy suffers,as the type 2 display displays poles nearer the vanishing point than the type 1 for a-given physical size. We can, however, make a parallel-type displaylarge-enough-that it has this same sensitivity. The vani-shing.:point for the peripheral display does not change with yaw, although the

vani-shi~g pQint of the simulator-and-the CRT display does. Because a reasonably large

physical size is desirable from a psychological point of view, the type 1 unit was chosen for-the simulation at present . . The possibility remains open that the type 2 unit may be used if it is found that the psychological need is not as great as expected; The display layouts resulting from these compromises are shown in Fig. 32-for-the type one~and two units.

6.7 Noise

It should be noted here that with the high speed gear train used in the displays, -noise can be_ a distracting problem. A high accuracy gear train should be used since standard "hobby quality" serve gear trains as employed at present are qui te noisy.

7. PlWBLEMS OF THE SIMULATION

We have several major problems in this design, none insurmountable. They

include:

7.1 _Accuracy of PeripheraLSpeedControl

Accuracy of speed control on the peripheral display is not as good as might be hoped. It is, however, sufficiently accurate that its design function is realized. An 'internal transformation (i.e., in the computer) to take care of nonlinearities in

the voltage-velocity function aidstremendously. A graph of this function and a fitted curve is shown in Fig. 33.

7

.2_:Intermittent Nature:of-,the Display

The intermittent updating nature of the display system introduces a

prob-lem into the viewing and the equations. If the update is too infrequent, then the

pilot-will-not be able to'control the vehicle. If the frequency input as a distur-,bance:contains high frequencies~ since they cannot be displayed, they are lost to

thepilot who is simply unaware of'their existence. He cannot of course track this signal as aresult. Compounded with-this problem is-the fact that the pilot visually -_ : samples -himself, and is' thus subject to the same sort of limi tations. The cri tical

frequencies in the pilot sampling case are qui te high ,however .

_The updating introduces a delay into the equations as well, since the loca-'_ :tion _is inputted to the computer, and af ter a delay is plotted. The amount of the

'. ': 'delay depends on the calculation time.

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