Tracking curved trajectories with a tunnel-in-the-sky display

17th European Annual Conference on Human Décision Making and Manual Control

TRACKING CURVED TRAJECTORIES WITH A

TUNNEL-IN-THE-SKY DISPLAY

Max Mulder *

* Delft University of Technology, Faculty of Aerospace

Engineering, Control and Simulation Division

P.O. Box 5058, 2600 GB Delft, The Netherlands

E-mail: m.mulder@lr.tudelft.nl

Abstract: The tunneî-in-the-sky display is a viable candidate to become the primary flight display of future aircraft cockpits. The tunnel display shows the fiight trajectory to be flown in a synthetic three-dimensional world. Presenting the guidance informa-tion via spatial sources of informainforma-tion has important conséquences for a pilot. Hence, to understand pilot manual control behaviour with a perspective display, it is essential to investigate the manner in which pilots use thèse optical eues. The paper describes the approach chosen and discusses one of the experiments.

Keywords: Aircraft control, cockpit displays, information analysis, cybernetics.

1. T H E TUNNEL-IN-THE-SKY DISPLAY The volume of air transportation will show a considerable growth in the near future. New technologies are being developed with the dual objective of increasing the efficieney of

air traffic management

and enhancing fiight

safety. One of the expected measures is to

increase the flexibilíty in air trame control by allowing curved approach profiles. Flying these - inherently more complex - curved approaches increases the pilot task demand load and requires enhanced levéis of situa-tion awareness. Improving the presentasitua-tion of information to the pilot by means of in-tuitive displays can alleviate these problems considerably (Oliver, 1990). A promising can-didate to become the primary flight display of future cockpits is the

tunnel-in-the-sky

dis-play (Fig. 1), which shows a spatial analog of the planned trajectory. Previous research indicated that the tunnel display has

cer-tain advantages over current flight displays in both the pilot manual as the supervisory task (Wilckens, 1973; Grunwald, 1984; Wickens, Haskell, & Harte. 1989; Theunissen, 1997). A perspective flight-path display, showing the planned trajectory to the pilot in a synthetic three-dimensional world is not a new concept. Since the late 1940's it has been hypothesised that such a pictorial display could mean, in many ways, an important improvement in information-transfer to the pilot. Its applica-tion was impractical, however, due to techni-cal limitations. Basitechni-cally, two developments in technology made the pictorial display concept practical. First, rapid improvements in com-puter technology made sufficiently detailed real-time graphics possible. Second, the ad-vance of new positioning systems such as GPS (Global Positioning System) provided the ca-pability of accurately measuring the position of the aircraft with a sufficient update rate.

Fig. 1. The tunnel-in-the-sky display.

The application of a perspective display in the cockpit has important consequences. In a conventional cockpit the pilot mentally re-constructs the aircraft's spatial and tempo-ral situation from a number of planar, i.e. two-dimensional, displays. With a perspective flight-path display this information is pre-sented in a

spatial

format (Mulder, 1995). At the Delft University of Technology a re-search project was initiated to investigate the applicability of a tunnel display for the pi-lot manual control task. In contrast to other studies the project goal was not to compare the tunnel display with current displays in terms of pilot performance, situation aware-ness, and workload. Rather, the objective was to obtain an understanding of how pilots use the tunnel display as their main source of information in the aircraft guidance task (Mulder, 1995). Once this understanding is achieved, an attempt can be made to repre-sent the important characteristics of the pilot in a mathematical model. For this purpose, a methodology has been developed, labelled the

cybernetic approach,

which allows sub-stantial insight into the effects of varying display designs on pilot behaviour (Mulder. 1999). Four main steps can be distinguished in the approach: (i) a description of the pilot tasks; (ii) an identification of the interaction characteristics of the pilot and the display,

leading to theoretical implications; (iii) an experimental validation of these theoretical implications, and (iv) an attempt to describe the observed pilot behaviour in a mathemat-ical model (Mulder & Mulder, 1998).

The paper will discuss the characteristics of interaction and an experimental assessment of the pilot task of manually guiding the aircraft along a circular tunnel trajectory.

2. T R A C K I N G CURVED

T R A J E C T O R I E S

The pilot's task is to follow a planned ref-erence trajectory, a typical guidance task. Based on the characteristics of this reference trajectory, the guidance task can be divided into a number of sub-tasks (Mulder, 1995):

(i) to maintain or track a straight section of the trajectory; (ii) to maintain or track a curved section of the trajectory, and (iii) to control a transition between a straight and a curved section of the trajectory. In other words, or, from a system-theoretical point of view, following the planned trajectory leads to maintaining a series of different system steady-states (or references) and controlling transitions between these steady-states. The research project has been defined ac-cording to these different pilot sub-tasks. In (Mulder, 1996; Mulder & Mulder, 1998) the

17th European Annual Conference on Human Décision Making and Manual Control

behaviour of a pilot Controlling the aircraft along a straight section of the trajectory has been examined. In (Mulder & van der Vaart, 1998) the behaviour of a pilot C o n t r o l l i n g the aircraft in a curve-interception manoeuvre is analysed. The current paper deals with the sub-task of Controlling the aircraft along sec-tions of the trajectory that are circular, i.e. curved with a constant radius.

3. O P T I C A L INFORMATION IN CURVED T U N N E L SEGMENTS

3.1 General

A perspective fiight-path display shows the trajectory to be followed in a synthetic three-dimensional world. The task of the pilot is to control the aircraft along this trajectory. To fulfil this task, the pilot estimâtes the state of the aircraft with respect to the trajectory and, based on this estimated state, décides upon and activâtes the necessary control actions. In order to understand the interaction be-tween the pilot and the display it is essential to understand this

state estimation process.

This has been investigated from two different points of view.

In (Mulder, 1994) it was examined what ef-fects a spatial display could have on the con-trol behaviour of a pilot: the H U M A N in the human-machine interface was taken to be the central element. Main questions that were addressed were the availability, the usefulness and the potential utilisation or

information-processing

of all sorts of spatial, or optical sources of information present in the real world and/or in a perspective display. In (Mulder, 1996; van der Hoek, 1997b; Mul-der, 1999) the M A C H I N E side was the main issue. An attempt was conducted to make an inventory of ail spatial eues in a generic per-spective flight-path display. Hère, irreper-spective of the human element, mathematical relations axe derived that express the state of the air-craft with respect to the référence trajectory in terms of these optica! cues:

information-transfer.

Based on these investigations from both a human as a machine-centered perspective, the

interaction characteristics

were put into a

theoretical framework (Mulder, 1999). For the three subtasks specified in §2, this framework led to a substantial insight into what design variables of the tunnel display were important to consider experimentally. NM1 ^ — — • " / \ P \ / \

\ ^ wjëEÈ

\_y © T — \ \ O ) — - — ' \ \ \ \

Fig. 2. A snap-shot of the tunnel image when

flying through a curved tunnel section.

Besides the éléments referred to in the

text, ® shows the horizon line, © the

fixed aircraft référence symbol and ® to

© the frame numbers f.

3.2 Curved tunnel sections

The analysis of optical information for the

curvi-linear

référence fiight condition along a circular trajectory begins with defining a generic tunnel. Fig. 2 shows the tunnel image corresponding with the situation considered here. The optical eues originate from the pro-jection of the main éléments of the tunnel

geometry - the

frames

© , the altitude

pôles

® and the

longitudinal Unes

© Connecting the frames - on the viewplane. An important dif-férence between the current situation and the case of straight tunnels, reported in (Mulder, 1996) is that, when looking farther into the tunnel, the tunnel geometry does not vanish to infinity but bends off towards one of the sides of the viewplane. A gênerai geometri-cal définition of a right curve is reported in (Mulder, 1999). It is assumed that the circular trajectory (radius i?t) is approximated by a concaténation of straight segments Si bridging an angular distance A $ , measured along the tunnel centercircle. The aircraft is positioned in the tunnel (tunnel width Wt, height Ht)

with an arbitrary position and attitude with respect to the tunnel centercircle. The downs-lope rt of the trajectory is assumed zéro.

3.3 Information-transfer

3.3.1.

Static optical eues

Positioning the aircraft with an arbitrary position error and attitude with respect to the trajectory results in a tunnel image similar to that of Fig. 2. The primary static eues are described at the hand

V'

h

hv

(a) The longitudinal tunnel cues

(l)-(4)-(b) The lateral tunnel cues (5)-(7).

Fig. 3. Two subsets of static optical cues in a curveé tunnel section. The (U,V) and (17', V') axes

represent the fixed and rotated central viewplane axes, respectively.

of Fig. 3 showing two subsets of cues resulting from the projection of the longitudinal (Fig. 3(a)) and vertical (Fig. 3(b)) éléments of the tunnel geometry1. The following cues can be defined (Mulder, 1999):

(1) The

distance (angular)

into the tunnel

Smax (amax^ d e£n e (j a s t^e maximum

1 T h e cues resulting f r o m the projection of the l a t

-eral elements of the t u n n e l geometry - the vertical

displacement cues - are s i m ï l a r t o those of straight

t u n n e l segments ( M u l d e r , 1996; M u l d e r & M u l d e r , 1998).

distance along the tunnel centercircle that is visible on the viewplane.

(2)

The position of the infinity points (u

ca

,v

00

)

s

.

that result from extrapolating the four longitudinal segment lines - for each seg-ment s¿ - to infinity.

(3) The

relative distances

between the infin-ity points (AUOOJ Auoo)s. s. of segments

Si and Sj.

(4) The

optical splay angles

( f i í . . . ^ . defined as the angles of the longitudinal segment lines of segment s¿ with the horizon.

17th European Annual Conference on Human Décision Making and Manua ontro

(5) The

latéral displacements ej

i (left),

n^

(right) and T i / , (poles) of the vertical frame lines and the altitude poles of frame fi with respect to the rotated viewplane centerline V'.

(6) The relative latéral displacements ej

i

j

i

(left). T]fifj (right) and nfifj (poles) of

the vertical frame lines and the altitude poles of frames fi and fj.

(7) The position of the

tangent point

on the viewplane, defined as that point of the inner curve tunnel wall which has the smallest latéral displacement n = nTP.

An important différence with the inventory of static cues for straight tunnels is that instead of only one infinity point and one set of splay angles, the curved trajectory yields similar quantifies but now for all tun-nel segments sj. Fürther, because the circu-lar trajectory is shown through a concaténa-tion of straight segments, no pseudo-horizons

(Mulder & Mulder, 1998) émerge in the dis-play. Mathematical expressions are derived

(van der Hoek, 1997b) that relate the opti-cal cues to the aircraft state with respect to the circulai tunnel trajectory. For a formai mathematical description of the array of cues listed above, the reader is referred to (Mulder, 1999).

3.3.2.

Dynamic optical cues

The dynamic optical cues are essential in the perception of two important referents of curvi-linear mo-tion, i.e. the

flight-path angle

and the

yaw-rate.

Whereas the yaw-rate can in principle be estimated with static cues, the flight-path angle can not. In (Mulder, 1999) it is shown that there are two, essentially identical forms of dynamic optical cues. First, there are the derivatives of the static optical cues, labelled the

indirect

dynamic cues. Second, there are the direct dynamic cues originating from the global optie flow field.

The derivatives of the static cues provide information about the flight-path, the yaw-rate and the radius of the curvi-linear motion. A yaw-rate error can be perceived as the translational velocity of the complete tunnel geometry on the viewplane. It can be hypoth-esized, although the perspective projection atténuâtes some of the error magnitudes, that for curvatures which are not extremely shal-low the yaw-rate error is especially salient at larger viewing distances.

The flight-path angle error is conveyed by

Fig. 4. The optie flow field for a curvi-linear

motion condition with a yaw-rate that is

too small and a flight-path angle error to

the left. The circle shows the direction

of the velocity vector with respect to the

World. The thin lines, the dash-dot line

and the dashed line show the theoretical

flow pattern, the locomotor flow line and

the reversai boundary respectively. (the

following state is plotted: Kt—2000 [mj;

W

t

= H

t

=45 [m]; V

tas

=70 [m/s];

X

e =

- 5 ° , ib

e

=0°; 0=0°; <P =

7 ° ; X

e

=0 [m])

similar cues as in straight tunnel sections. For small viewing distances S4, the derivatives of the splay angles and the relative latéral displacements of the tunnel frames are only a function of the flight-path angle error. An important différence between the condition of straight tunnels, however, is that in curved trajectories no (stationary) vertical pseudo-horizon exists that could facilitate the use of the relative latéral displacement rate cues. The curvi-linear motion condition leads to a hyperbolle optie flow field that can be seen as the sum of two components, i.e. a

transla-tional

component yielding a radial expansion

pattern, and a rotational component yielding a

solenoidal

flow pattern (Prazdny, 1981). The addition of both flow patterns implies

that

no focus of radial outflow is present in

the flow field

(Gordon, 1966). Rather, the entire flow field is curved into the direction of the curvi-linear motion as shown in Fig. 4. The curvi-linear field resembles the radial field near the observer where the effects of the translation are large. For larger viewing distances the rotational effects overshadow those of translation (Gordon, 1966). When the yaw-rate is too small, the flow velocities decrease in magnitude, especially for larger viewing distances St: the tunnel image does not show the desired translatory motion and

the percept will be one of going off the tra-jectory. The effects of a flight-path angle error are especially salient near the observer. The effects of errors in yaw-rate and in flight-path angle can either amplify or attenuate each other, illustrating the difHculty of conceptu-alizing the optie flow in curvi-linear motion.

3.4 Information-processing

The study of curvi-linear motion is far more complex than that of the rather elementary recti-linear motion condition. In the previous subsection the tunnel display was analyzed mathematically in order to investigate how the aircraft motion referents are presented. Based on these results and a literature sur-vey on human visual motion processing the optica! cues are analyzed from a pilot's per-spective in (Mulder, 1999). Some of the main findings are briefly summarized below. In the control task of maintaining a curvi-linear flight condition, a pilot needs to mon-itor a number of aircraft states. The aircraft

angle of roll 4>

- presented with the horizon line - is important as inner loop attitude control variable. The

yaw-rate error r

e is a

function of the error in aircraft roll attitude, but can also be perceived by the sweeping translational motion of the whole tunnel on

the viewplane (the derivative of S™ax). The

required yaw-rate can be perceived by the cur-vature of the trajectory for which the relative distances between the funnel frames {nf^-,

ef

i

f

j and 7Tƒ;

f. )

and the various infinity points

((Auoo, Avcx

f)

s

.

s.)are the most likely cues. Because the yaw-rate is the main cause of solenoidal flow, a strong radial flow is an important cue for a too shallow curve. In the absence of a Singular infinity point (or pseudo-horizon) the aircraft

heading angle

error

ipe, defined relative to the tangent to the centercircle, must be perceived through the lateral translation of the tunnel geometry as a whole. Especially the tunnel geometry displacements for larger viewing distances St - further into the curve - are important. The

position error X

e can be perceived through

the splay angles of the longitudinal lines

((^I..A)S.) and with the relative

displace-ments of the tunnel frames (J?/;/,-, Cfif5 and

Ttfifj), especially those close to the viewpoint (small St). Due to the trajectory curvature,

however, no lateral

pseudo-horizon

exists in the display, which could impede the use of

the compression gradients considerably. Fur-thermore, in (Mulder, 1999) it is shown that due to the perspective projection, the part of the trajectory closest to the viewpoint is not shown. Hence, the perception of both the aircraft heading angle error and the lateral position error could be considerably

biased.

The

flight-path angle error

Xe

oi

the aircraft, or, the instantaneous direction of the curvi-linear motion with respect to the tangent of the tunnel centercircle, can be perceived with the global optie flow field and/or the gradients of local éléments in the visual field. In (Mul-der, 1999) it is argued that it are especially the

local gradients

of motion perspective that form the basis of flight-path estimation. In this respect, similar cues play a role as in straight tunnel sections, i.e the splay angle rates and the compression rates.

3.5 Pre-expérimental hypotheses

Similar to the situation for straight segments of the tunnel trajectory (Mulder, 1996), the two primary cues for aircraft position and flight-path with respect to the trajectory are those of optical splay and optica! density. The main différence, however, is that in curved tunnels

no symmetrical condition, yielding

the important pseudo-horizons, exists

which probably hampers the use of the density cues.

Obviously then, one could hypothesize that the tunnel contour - providing splay - forms the basis for accurate path following perfor-mance. Presenting only splay, however, could lead to a significantly biased perception of lateral position, a bias which can be decreased considerably when presenting frames. Hence, it is important to assess the relative usefulness of the tunnel contour and the tunnel frames experimentally.

4. E X P E R I M E N T

4.1 Goal of the experiment

An experiment has been conducted to investi-gate the effects of various tunnel design vari-ables on pilot performance, control activity, control behaviour, and mental workload in the pilot guidance task of following a curved trajectory. Hence, in the line of the cyber-netic approach the goal of the experiment was

17th European Annual Conference on Human Decision Ma ing an

i anua ontro

Fig. 5. The experimental tunnel display characteristics (no rotation of the tunnel).

twofold. First, the validity of the

hypothe-ses originating from the information

analy-sis, discussed in the previous section, must

be examined. Second, the observed control

behaviour of the subjects must be described

with a mathematical model. The present

pa-per is restricted to the statistical analysis of

all measured data (van der Hoek, 1997a). For

a detailed discussion of especially the

model-based analysis the reader is referred to

(Mul-der, 1999).

4.2 Method

4.2.1. Apparatus and setup Subjects were

seated in a chair in a darkened, noise-free

room in front of a 17 inch CRT monitor. The

control manipulator was a servo-controlled

hydraulic side-stick with common

character-istics. The display update-rate was 20 Hz.

The tunnel was presented as a grey wireframe

on a black-and-white background. A

flight-path vector was presented that showed the

instantaneous direction of motion.

The lateral/longitudinal aircraft motions of a

small business jet, a Cessna Citation I, were

simulated in the experiment. The aircraft

mo-tions were disturbed with two independent

random disturbance signais, representing a

relatively strong atmospheric turbulence field.

There was no side-slip, i.e.

Xe

4.2.2. Subjects and instructions to subjects

Four professional pilots participated in the

ex-periment. They were instructed to control the

latéral/longitudinal aircraft motion through

the tunnel as accurately as possible.

4.2.3. Independent measures Three

inde-pendent measures were manipulated in the

experiment. First, to examine the validity

of the pre-experimental hypotheses

originat-ing from the information analysis, five

dif-ferent tunnel display geometries were denned.

These geometries, illustrated in Fig. 5 are

all abstractions of a generic

tunnel-in-the-sky display. Display A is the baseline tunnel.

Displays C and D are the same as A except

that display C shows no tunnel frames while

display D shows no tunnel contour. Displays

B and E are the same as, respectively,

dis-plays A and D , except that the tunnel frames

are separated with a randomized inter-frame

distance (Table 1).

The second independent measure was the fact

whether the tunnel geometry was rotated as

a whole, or not. In the absence of wind, an

aircraft makes a co-ordinated turn at a

con-stant yaw-rate with a concon-stant roll angle. This

reference roll angle can be presented

pictori-ally by means of rotating the tunnel geometry

around its central axis (see Fig. 6). Earlier

research showed (Grunwald, 1996) that

rotat-ing the tunnel with the reference aircraft roll

angle could improve pilot performance.

The third independent measure was the

aircraft velocity. Two velocities were

simu-lated, 70 and 110 [m/s], representing an

ap-proach and cruise velocity, respectively.

4.2.4. Design The expérimental design was

a 5 x 2 x 2 factorial design (display. frame

rotation, aircraft velocity), yielding 20

conditions. Every condition was conducted 12

times: the first six runs were training runs and

the last six runs measurement runs. The 20

conditions were randomized over ail 240 runs.

1 Ith European Annual Conference on Human Décision Making and Manual Control

Table 1. Expérimental tunnel

geome-tries.

t u n n e l t u n n e l t u n n e l frame d i s p l a y c o n t o u r frames p o s i t i o n i n g A yes yes r e g u l ä r B yes yes r a n d o m C yes no -D no yes r e g u l ä r E no yes r a n d o m no rotation rotation

Fig. 6. Rotation of the tunnel geometry with

the référence angle of roll.

4.2.5. Dépendent measures Seven aircraft motion states were selected as dépendent measures: (i) the pilot's control signal 5a and

its derivative öa; (ii) the différence between

the aircraft angle of roll and the référence angle of roll, <be and its derivative p; (iii) the

heading angle error ipe and its derivative, the

yaw-rate error re; and (iv) the cross-track

error Xe. The Standard déviations of these

Signals were used in a Statistical analysis. Be-cause in some conditions the cross-track error was considerably biased, both the standard déviation Xe—S as the root-mean square Xe—

R were computed, yielding a total of eight

independent measures. In this paper only a few of the main Undings will be discussed.

4.2.6. Expérimental hypotheses Rotatingthe tunnel geometry with the référence aircraft angle of bank can be expected to help the pilot in Controlling this variable and, as a conséquence, maintain the right turn rate. This is hypothesized to be especially helpful when the yaw-rate is hard to estimate, i.e. for displays D and E . At the same time, however, the atmospheric disturbances lead to drifting aircraft motions away from the référence tra-jectory. Because the pilot task is to minimize ail path-following errors, requiring continuous (small) roll angle adjustments. Therefore, the intended virtue of the tunnel rotation might not show up at all in the experiment.

Concerning the various displays it is clear that the main interests are the effectiveness of the tunnel frames - conveying optical den-sity - vs. the tunnel contour - conveying optical splay - and the effect of regulär vs.

irregulär frame positioning. The information analysis revealed that it can be hypothesized that following the curve in terms of flight-path error ipe would probably be superior for

the splay-only display (C). Due to a biased présentation of lateral position, however, it is hypothesized that path-following accuracy in terms of lateral position error Xe: might be

inferior for this display. It is hypothesized fur-ther that frame irregularity is detrimental for performance when no contour is available ( E ) , especially because of the total lack of splay and splay rate information in this display.

5. RESULTS AND DISCUSSION The rotation of the tunnel had no signifi-cant influence at ail on pilot path-following performance. It did not lead to a decrease of the lateral position and flight-path angle errors. Rather, performance became worse. The tunnel rotation did lead to a significantly lower variation in the roll angle error 4>e for

ail displays except display C , indicating that 4>e was being controlled more actively when

the tunnel was rotated. The non-significance of the r o t a t i o n effect in ail other cases al-lows the rotation measure to be discarded from further analysis, limiting the expérimen-tal conditions to 10 (velocity (2 levels) and display (5 levels)).

The means and 95% confidence limits of ail eight experiment dépendent measures (ail subjects) averaged over the 10 expérimental conditions are illustrated in Fig. 7. As one can see from this figure, the higher velocity condition leads to lower pilot control activity (<^a> àa) , higher aircraft roll angle and roll

rates (ée, 4>e): lower heading angle (ipe) and

yaw-rate (re) errors, and to somewhat higher values of the lateral position error measures

(Xe — S. Xe — R). These effects can be partly

attributed to the different aircraft handling characteristics for the two velocity conditions, and the fact that especially the amplitudes of the dynamic optical eues are a linear fonction of the velocity of motion.

Results indicate that heading angle tracking accuracy is superior for the splay-only display (C). Position error performance is also quite good with this display, but only in terms of the STD (Xe - S). Comparing Figs. 7(e) and

7(f) reveals that the use of this display leads to the largest bias of ail displays in Controlling the lateral position relative to the centercircle.

17th European Annual Conference on Human Décision Making and Manual Control

co - O co 70 A B Cp D E

i no

i 1 ; A B C D E , 10 bO c ; 55 7

I

[ 70 j -A B CE D n — 1

no

I—• A B e D E

(a) aileron (b) roll angle error

i tu A Q ' 1 7 0 1 Á B C D E

rao

A B C _{D E}

I !

1.4 1.2 •s-1.0

o

fr- 0.8 eo ï \ i 1I

i

" í i ! ^ ] ! $ Ti ! 5 -i Í ; I 70 I A B Ç D E I 110 I i A B <t D E (c) roll angle error derivative (d) heading angle error

a C D E i n o

r

A B C A É 1 1

_{! 1}

T 1 ! ! Í I! 1 ! ! ! ! _{1 i}

S

! i|i

î

E

i

I ! I ! I

Ë

ï ï ! i ¿ 1 70 1

1

y $ Ç D E j

1

no

1 A B C I > I ;

(e) S T D position error (f) R M S position error

Fig. 7. The means and 95% confidence limits of the experiment dépendent measures (ail subjects). In thèse figures the insets show the two velocity conditions (70 & 110 [m/s]). The codes of the five displays are shown at the bottom.

So, although pilots smoothly fly through the tunnel with this display, they adopt a con-sistent and most probably unperceivable bias towards the outer side of the curve. This bias also occurs for the other displays but to a significantly less extent, especially when no tunnel contour is presented at ail (displays

D and E ) . These data support the

hypoth-esis that the tunnel frames compénsate for the position error bias caused by the optical splay information. The results further support the hypothesis that when no tunnel contour is available the accurate control of the roll angle becomes more important in order to maintain the right yaw-rate (Figs. 7(b) and 7(c)). Flight path control détériorâtes with these displays ( D and E ) , caused by the lack of splay information and the ineffectiveness of the information conveyed by the tunnel frames for this purpose.

Finally, frame irregularity shows to be of only minor importance when splay information is available. When the splay cues are not avail-able performance decreases rapidly when the

frames are put in random order. Although not shown in Fig. 7 it are thèse conditions where the rotation of the tunnel geometry as a whole had the largest - but not significant - positive effect on pilot path-following performance.

6. C O N C L U S I O N S

The experimental data show that the primary cues used by pilots to control the aircraft along curved tunnel segments, are the optical splays conveyed by the longitudinal tunnel contour lines. The use of splay angles and es-pecially the splay angle rates leads to smooth trajectory following, but, due to the introduc-tion of perceptual biases, not with the best performance. The optical density information conveyed by the tunnel frames forms a second piece of information used by pilots. Control with frame-only displays is less smooth, more jerky, but has the advantage of much smaller perceptual biases leading to improved path-following performance. The combination of

both sets of cues in the baseline generic tunnel geometry yield the best performance. Rota-tion of the tunnel geometry with the datum aircraft roll angle does in general not lead to increased path-following performance. Al-though the roll angle itself is controlled more accurately, the virtues of tunnel rotation for performance only occurs in the information-poorest tunnel geometries.

7. A C K N O W L E D G E M E N T S The author wishes to acknowledge A J van der Hoek, M.Sc. student, whose graduation thesis work provided the basis for this paper.

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Proceed-ings of the XVth European Annual

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