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FORMAL ARTICLES
Theoretical Foundations for a Total
Energy-Based Perspective
Flight-Path Display
Matthijs H. J. Amelink
DECIS Lab
Thales Research and Technology, The Netherlands
Max Mulder and M. M. (Rene) van Paassen
Department of Aerospace Engineering
Delft University of Technology
John Flach
Department of Psychology
Wright State University
One of the most difficult aspects of manually controlled flight is the coupling between
the control over the aircraft speed and altitude. These states cannot be changed inde-
pendent of each other through the aircraft control devices, the elevator and the throt-
tle. Rather, to effectively change an aircraft’s speed and altitude, the controls have to
be coordinated. The mediating mechanism that underlies the coordination of the con-
trols is the management of the aircraft’s energy state. This article shows that the ab-
straction hierarchy (AH; Rasmussen, 1986) framework can be effectively used to gain
more insight into the underlying structure of the aircraft energy management prob-
lem. The derived AH representation is based on the analysis of the energy constraints
on the control task. It reveals the levels of abstraction necessary to link the aircraft’s
physical controls to the speed and altitude goals and also how the aircraft energy is a
critical mediating state of the control problem. Energy awareness can be increased by
presenting explicit energy management information. The powerful and novel con-
THE INTERNATIONAL JOURNAL OF AVIATION PSYCHOLOGY, 15(3), 205–231
Copyright © 2005, Lawrence Erlbaum Associates, Inc.
Requests for reprints should be sent to Matthijs H. J. Amelink, DECIS Lab Delftechpark 24, 2628
XH Delft, P.O. Box 90, 2600 AB Delft, The Netherlands. Email: Matthijs.Amelink@Decis.NL
cepts of the total energy reference profile and energy angle are introduced in this arti-
cle and applied in the context of a perspective flight-path display. The resulting dis-
play presents energy management information fully integrated with the
tunnel-in-the-sky display and reveals 5 new and important energy cues, intuitively
linking the controls and the goals.
In his classic textbook on piloting, Stick and Rudder, Langewiesche (1944) used
a concept called lift. This is not the lift force generated by the wings as analyzed
in aerodynamics and aeronautical engineering. Rather, Langewiesche used it to
illustrate an aircraft’s potential to fly. He wrote that an aircraft with lots of lift is
safe because the aircraft can easily gain altitude or pick up speed, whereas an
aircraft with a lack of lift is very limited in maneuvering. The concepts taught in
Langewiesche’s book today still help student and accomplished pilots better un-
derstand the airplane. This article, like Langewiesche’s book, strives to provide
a deeper understanding of the airplane and the task of flying, but in a cognitive
systems engineering context. The key concept of lift that Langewiesche dis-
cussed is here identified as total energy. Total energy is the sum of the aircraft’s
kinetic energy, which is the energy of the aircraft’s speed, and the potential en-
ergy, the energy in the aircraft’s height. We show that understanding the energy
management in flight is essential to a deep understanding of flight control.
With few exceptions,1today’s modern cockpit does not support the concepts of
total, potential, and kinetic energy, although they could be of use in learning and
performing the task of flying. The introduction of energy-related information in
future guidance displays, such as the tunnel-in-the-sky display, has been reported
by Theunissen and Rademaker (2000), who adopted a basic, symbolic presenta-
tion that is common practice in head-up displays (HUDs; Newman, 1995). Simi-
larly, Sachs and Sennes (2001) reported a control-theoretical analysis of further
augmenting the HUD-like symbology for energy management.
In this article, a more fundamental and novel approach is chosen. We explore
Rasmussen’s (1986) abstraction hierarchy (AH) as a framework for modeling the
task of flying. Other descriptions of the piloting task, often based on dynamic con-
trol-theoretic models, only describe the machine’s behavior, not the machine’s
functions and their relation to the goals to be achieved. In contrast to this, the repre-
sentation of the energy management task in the AH provides the link among the
task objectives; the management of kinetic, potential, and total energy; and the
control possibilities (Amelink, van Paassen, Mulder, & Flach, 2003a). Our under-
standing of the flight task, mapped in the AH, is then used as the avenue for com-
206 AMELINK, MULDER, VAN PAASSEN, FLACH
1Some sailplanes are equipped with a total-energy-based climb indicator, which shows total energy
gains and losses as a climb or descent speed; that is, in the units of potential energy rate.
A demonstration version of the energy display can be downloaded from http://www.amelink.net/
mscthesis.
municating these concepts to pilots, by designing a display that shows the energy
relations and their relevance to the flight goals, using the paradigm of ecological
interface design (EID; Vicente & Rasmussen, 1992). By mapping the domain con-
straints to the pilot interface, the AH can become an externalized mental model to
enhance pilot energy awareness and energy management (Amelink, van Paassen,
Mulder, & Flach, 2003b).
The article consists of two parts. In the first part, the mapping of the flight task
to the AH is described. The second part of the article discusses the en-
ergy-augmented perspective flight-path display and the translation of the AH map-
ping to this display.
SCOPE OF THE WORKSPACE ANALYSIS
Flach et al. (2003) described a first attempt to capture the task of landing in the
AH framework, and for our analysis, this article is used as a starting point to fur-
ther elaborate the role of the energy constraints. The analysis in Flach et al. took
a broad view of the flying task, illustrated by the fact that safe flight was identi-
fied as the top goal. A more restricted scope is used in this article.
The top level of the AH, the functional purpose level, defines the system’s goal
in the environment. A precise definition of the system boundaries will lead to a
better insight into the system that is being analyzed. Our interest is the role of en-
ergy during the precision landing task and the system goals and boundaries should
reflect that. There are basically two goals that the pilot has during (symmetric)
flight: following a certain speed profile and following a certain altitude profile. Of
course, other tasks, like managing the fuel systems, are needed for the aircraft to
function as a whole, but these are left out of consideration in this article. Thus, the
functional purpose level is defined by speed and altitude profiles that need to be
flown.
On the other end of the AH we find the aircraft-dependent levels, the physical
form level and the physical function level, that deal with the physical implementa-
tion of the aircraft system. On these levels are, among other things, the manipula-
tors the pilot has for the control of symmetric flight: the throttle and elevator. The
coordination of these controls to achieve the speed and altitude goals was one of
the main points of interest for Langewiesche: The student pilot has a throttle and an
elevator to control speed and height, but which manipulator controls what? The
answer is that neither one controls the aircraft speed or altitude independently from
the other. Rather, they must be used in coordination. We believe that the key to the
coordination of the manipulators lies in controlling the energy state of the aircraft,
and this is what should be on the middle levels of the AH. These levels link the
means (throttle, stick or elevator) and the ends (target speeds and altitudes) using
energy relations. An analysis that makes these relations explicit can be used as a
basis for an EID (Vicente, 2002). This approach to flight interface design can be
TOTAL ENERGY-BASED FLIGHT-PATH DISPLAY 207
considered a complement to the development of automatic flight control systems
by Lambregts (1983), who also recognized the role of energy in flight control.
CONTROL TASK ANALYSIS
Observed Pilot Control Strategies
During the approach the pilot manages the aircraft state to comply with the
speed and altitude goals set by a predetermined trajectory. Atmospheric distur-
bances interfere with accomplishing these goals and force the pilot to take cor-
rective actions. Depending on the type of aircraft and landing situation, the pilot
generally applies one of two control strategies. In the first control strategy, the
pilot uses the throttle to control the vertical flight path (altitude) and the elevator
to regulate speed. This strategy is referred to as throttle-to-path and eleva-
tor-to-speed. In the second control strategy, the pilot uses the elevator to control
the vertical flight path and the throttle to control speed. This strategy is referred
to as throttle-to-speed and elevator-to-path. These reflect two different
coordinative structures, in terms of which degrees of freedom are locked out and
which degrees of freedom are controlled (Bernstein, 1967).
In principle, either strategy might be used to land. However, from discussing
the issue with pilots, there appear to be clear preferences. The elevator-to-speed
mode seems to be preferred for standard runway approaches (e.g., commercial avi-
ation), whereas the throttle-to-speed mode seems to be preferred for approaches to
shortened runways (e.g., aircraft carriers, general aviation). The focus of this anal-
ysis is on a landing to a standard precision runway, which is typical for commercial
and general aviation. The analysis assumes zero-wind conditions. However, we
suspect that specification of the energy state may be particularly valuable in vari-
able wind conditions.
Means for Controlling Energy
Speed and altitude are directly related to the total and potential energy of the air-
craft. To understand the aircraft energy control one must first understand what
the energy relations are and how energy can be regulated. Kinetic energy is the
energy of a moving object and is a function of its speed, as shown by:
(1)
where mis the aircraft mass and Vthe aircraft’s velocity relative to the ground.
The aircraft’s potential energy is determined by its altitude above a ground ref-
erence such as the runway threshold, as shown by:
208 AMELINK, MULDER, VAN PAASSEN, FLACH
2
1,
2
kin
EmV=
Epot =mgh, (2)
where his the altitude above the reference and gis the gravitational acceleration.
The sum of the two energies is the aircraft’s total energy E. The law of conser-
vation of energy states that energy cannot be created or destroyed. This means
that when the total energy is constant, the kinetic and potential energies can
change but only in equal and opposite amounts. Thus, altitude can be traded for
speed and vice versa without gaining or losing total energy. Langewiesche
(1944) made this point when he wrote that speed = height and called it the law
of the roller coaster. The other implication of the law of conservation of energy
is that an aircraft can only lose total energy through drag: The energy is trans-
formed into heat, which is bled off to the surrounding air. The only way in
which an aircraft can gain total energy is through the energy added by the en-
gine. The net total energy flow into the aircraft is a function of the difference be-
tween engine thrust, T, and the aircraft drag, D:
(3)
where is the total energy rate. Except for the throttle, the pilot only has con-
trols to increase drag, which are of course used as little as possible. Therefore,
the engine thrust is the preferred way to control total energy, and because the
throttle controls the engine, the throttle becomes the aircraft’s energy control.
Thus, the throttle does not control speed or altitude like the two control strate-
gies already introduced imply, but rather controls the aircraft’s total energy rate.
What does the elevator do? It is reasonable to assume that the elevator has neg-
ligible influence on drag, as changes introduced by the flight control surfaces (e.g.,
elevator) are small relative to the total drag. Furthermore, when the maneuver rates
are small (as with commercial aircraft), the variations of induced drag can be ne-
glected as well. Thus, control of the elevator has negligible impact on total energy
or total energy rate. What it does do is exchange energy between kinetic and poten-
tial energy: It is the energy distribution device. This is where Langewiesche’s law
of the roller coaster comes into play: When using only the elevator to go up it will
be at the expense of speed; in a complementary fashion, speed can be gained at the
expense of height.
The Reservoir Analogy
The energy controls can be visualized as if the aircraft is a system holding two reser-
voirs. One contains the kinetic energy and the other the potential energy. Together
these reservoirs represent the total energy. There is one energy flow into the system
provided by the engine and there is only one energy flow out of the system through
TOTAL ENERGY-BASED FLIGHT-PATH DISPLAY 209
–,
ETD
V=
E
aerodynamic drag. The net energy flow results from the difference between thrust
and drag (Equation 3). This flow is then distributed over the kinetic and potential en-
ergy flows into and out of the reservoir. The throttle controls the valve regulating the
total energy flow into the system and the elevator controls the valve distributing the
energy flow. Figure 1 is a graphical representation of the analogy, showing the en-
ergy flows (the arrows indicate positive flows).
Energy Awareness and Energy Management
Although the pilot’s intentions are to control the aircraft speed and altitude, in doing
so he or she acts on the energy state of the aircraft. However, the pilot can only do this
effectively if he or she can identify the energy state. Most pilots have a gut feeling
about this, based on their experience, and feel safe when they have lots of energy.
They will avoid low-energy states because the lower energy boundaries are deadly.
Insufficient kinetic energy means that the aircraft is moving too slowly and is close
to a stall. A lack of potential energy means that the aircraft is dangerously close to the
ground. The combination of low and slow is especially dangerous because the pilot
no longer has the freedom to quickly pull up and gain altitude at the cost of speed to
avoid obstacles, or to dive and quickly pick up speed to prevent a stall. The pilot likes
to be fast and high, where there is lots of energy to exchange for safe maneuvering.
210 AMELINK, MULDER, VAN PAASSEN, FLACH
FIGURE 1 The reservoir analogy. The throttle regulates the total energy flow and the elevator
controls the energy flow distribution. In this figure, represent the total, potential, and kinetic en-
ergy rates, respectively.
This is a rudimentary form of energy awareness. When the pilot is flying a precision
approach, however, he or she will have to be able to identify the energy state much
more precisely to use the energy controls to correct deviations from the speed and
path goals.
It is common that the landing goals are defined as altitude and speed profiles.
However, it is also possible to frame the landing goals in energy terms. The target en-
ergy path would be a gradual reduction of total energy, so that a suitable energy level
is achieved at touchdown. When the pilot is confronted with deviations from the
commanded altitude or speed he or she somehow has to translate those deviations
into actions to be taken in terms of energy because the controls are energy controls as
shown by the reservoir analogy. This translation can be made by referring to the en-
ergy state matrix, Figure 2, which shows the possible energy state deviations of the
aircraft. On the vertical axis the total energy deviation ∆Eis the sum of the kinetic
∆Ekin and potential energy deviations ∆Epot on the horizontal axes. Each cell of the
grid represents a state deviation from the reference state defined by the total, kinetic,
and potential reference energies ∆Eref, , and , respectively.
Line A is the line of zero total energy error. Cells on this line have the proper to-
tal energy but the distribution of the total energy over kinetic and potential energy
may be inadequate. The solution to the problem is an exchange of energy that can
be realized by using the elevator. Deviations from Line A represent a total energy
error: When moving up in the energy matrix the total energy is too high; when
moving down in the matrix the total energy is too low. These deviations can only
be corrected by, respectively, decreasing or increasing the total energy using the
throttle. Generally, the pilot is required to coordinate the controls to bring the air-
craft into the right energy state.
Figure 2 provides a useful representation for understanding a typical heuristic
that some pilots use to solve the approach problem. Many of the pilots that we in-
terviewed reported that they set the throttle to a fixed level (e.g., in terms of engine
RPM) at the start of the approach and then use their elevator control to descend
along the glidepath with the proper airspeed. If the throttle setting is right, the total
energy will decrease at the same rate as the potential energy, which will bring
down the aircraft at a constant speed. Any altitude and speed errors (i.e., what we
now recognize as energy distribution errors) can be controlled using the elevator.
This also means that the errors are correlated; that is, when all goes well, you can
tell your altitude error (low or high) from your speed (fast or slow). Taking this line
of thought one step further, when the pilot perceives that the altitude and speed er-
rors are not correlated, he or she knows that the throttle setting must be wrong.
Dynamics and Cross-Coupling
Of course, an aircraft does not have actual valves to control energy as repre-
sented in the reservoir analogy. In this section we take a closer look at how the
TOTAL ENERGY-BASED FLIGHT-PATH DISPLAY 211
ref
pot
Eref
kin
E
energy relations are represented in the physical cause–effect relations among the
controls, the aircraft state, and the energy reservoirs. Figure 3 illustrates how the
controls affect the goals through the relevant state variables (Amelink, 2002).
The arrows represent causal links between control and state variables (i.e., how
one variable can influence the value of another), and these links may include dy-
namics. It is important to realize that the arrows do not represent energy flows or
forces.
There are three main areas of interest indicated by Boxes A, B, and C. Box A
shows how elevator inputs directly control the vertical flight-path angle γand the
altitude. Box B shows how throttle inputs lead to speed. This is how novice pilots
think of the controls. The complexity comes with Box C, which shows the energy
relations and forms the most important link between the direct elevator control
path (Box A) and the direct throttle control path (Box B). The link indicated with a
dashed arrow represents the cross-coupling of the aircraft’s pitching tendency due
to thrust changes. This cross-coupling may determine the preference for either
control strategy, as discussed at the end of this section.
Our main interest is in the role of the content of Box C. Again the law of conser-
vation of energy tells us that the energy rates must add up. The total energy rate is
the sum of the potential and kinetic energy rates:
(4)
In Box C the relations are drawn for a conventional generic aircraft. Because the
thrust acts more or less along the flight path it will first of all accelerate the air-
craft so that the total energy added to the aircraft wants to become kinetic en-
212 AMELINK, MULDER, VAN PAASSEN, FLACH
FIGURE 2 The energy state matrix translates speed and altitude deviations into energy devia-
tions. Line A indicates the situation of a correct total energy.
.
pot kin
EE E=+
ergy. This is represented by the arrow connecting and . However, the el-
evator can be used to achieve a certain vertical flight-path angle γthat is directly
related to the potential energy rate. In other words, the elevator can be used (in-
directly, through the aircraft’s flight-path dynamics) to demand a certain amount
of potential energy rate. The kinetic energy rate is a result of the total energy
rate minus the demanded potential energy rate. This is what the arrows in Box C
represent. Thus the elevator controls the speed indirectly.
In large transport aircraft, the added total energy due to throttle input tends to
become kinetic energy because the coupling represented by the dashed arrow in
Figure 3 is usually weak. For these aircraft the throttle-to-speed and eleva-
tor-to-path strategy may be preferred. Small trainer aircraft, however, have a much
stronger coupling as they commonly have the characteristic to pitch up when throt-
tle is applied. Thus, the throttle has a direct effect on the vertical flight path, and
therefore also on the potential energy demand, in the same way that the elevator
does. Going back to the reservoir analogy, one could say that in this case the throt-
tle also partly operates the energy distribution valve. Hence, for smaller aircraft the
throttle-to-path and elevator-to-speed strategy may be preferred.
Short-Term and Long-Term Control
From a pilot’s perspective, temporal dimensions exist in the control task as well:
short-term control and long-term control. The short-term control is the correction of
the state deviations. The controls are used for their direct effect as represented in Fig-
ure 3. Once the state deviations are corrected, the pilot wants to trim the aircraft, cre-
ating a steady flight condition at the commanded flight path and speed. This is what
TOTAL ENERGY-BASED FLIGHT-PATH DISPLAY 213
FIGURE 3 The cause–effect relations among the aircraft control manipulators (left) and the
pilot’s goals (right), characterized through the main aircraft symmetric state variables. These re-
lations reflect the so-called short period approximation of the aircraft vertical flight dynamics
(Brockhaus, 1994).
E
kin
E
pilots call stabilizing the aircraft, and it is referred to as long-term control. The con-
trols are no longer used for direct control but their settings have to be found that lead
to the desired steady flight condition. By definition the speed is constant in steady
flight. In Figure 3 this means that the kinetic energy rate has to be zero and that the to-
tal energy rate and potential energy rate must be equal (see Equation 4). Thus the
throttle has to be set to comply with the commanded vertical flight-path angle. For
long-term control the throttle and elevator need to be coordinated such that the eleva-
tor controls the vertical flight path and the throttle is used to match the total energy
rate to the potential energy rate demand.
ABSTRACTION HIERARCHY MAPPING
The AH has a number of important properties. First of all, each level is a com-
plete representation of the system under consideration. The level of abstraction
determines the view on the system and results in a set of terms, concepts, and
principles unique to that level. The relation between the levels was described by
Rasmussen, Pejtersen, and Goodstein (1994) as the why–what–how relation.
Each level has this relation with its adjacent levels. For example, looking at the
general function level in Figure 4 we find energy awareness and energy manage-
ment. The reason for energy management is defined one level higher, on the ab-
stract function level. The energy is controlled through controlling the right state
variables described on the physical function level. The upper levels of the AH
describe the goals and the lower levels describe the means available to achieve
these goals.
The scope of the analysis defines the top level of the hierarchy, which is the
functional purpose of the system. The lowest levels are defined to describe the less
abstract, physical implementation of the system’s function, the aircraft itself.
Therefore the top level and bottom levels are already defined.
The analysis in the previous section allows us to fill in the second (abstract
function) and third (general function) levels of the AH. Figure 4 shows the content
of each level related to the associated part of the analysis. The names of the levels
of the AH are adopted from Rasmussen et al. (1994) and their content becomes:
1. Functional purpose: The system’s meaning to the environment. The goal of
the aircraft, considering the task of manually controlling the aircraft longitudinal
motion, is to follow the altitude and speed profiles set by the nominal trajectory.
2. Abstract function and priority measures: The energy relations govern the
aircraft’s movement in the vertical plane. This level describes the energy laws that
the aircraft’s motion has to obey and centers on the law of conservation of energy.
The speed and altitude goals are expressed in energy goals. To satisfy the goals on
the level above, the energy goals have to be satisfied.
214 AMELINK, MULDER, VAN PAASSEN, FLACH
3. General function and work activities: These are independent of the physical
implementation. This level contains energy awareness (Figure 2) and energy man-
agement (Figure 1). The throttle is the aircraft total energy control and the elevator
is the energy distribution control. The control of energy rate yields control over the
aircraft energy state that has to satisfy the levels above.
4. Physical function and processes, equipment functioning: This level is de-
pendent on the physical implementation of the system. The above levels hold for a
generic fixed-wing aircraft, independent of the type of aircraft. On this level the
cause–effect relations of the aircraft-specific characteristics become important.
Examples of these characteristics are the pitching due to throttle control (e.g., the
dashed arrow in Figure 3) and drag variation with airspeed.
5. Physical form and configuration: This level contains a description of all air-
craft components. It is highly aircraft specific and is not discussed further here.
DISPLAY MAPPING: ENERGY
The functional purpose in the AH was defined as following a speed and an alti-
tude profile. To provide an intuitive mapping from the aircraft’s motion and po-
sition to the functional purpose of following an altitude profile, the design is
based on a tunnel-in-the-sky display, an egocentric perspective flight-path dis-
play that shows the trajectory to be flown in a three-dimensional format
(Mulder, 1999). Figure 5a illustrates the basic tunnel display that is the starting
point of the display design discussed here. The aircraft attitude, heading, speed,
and altitude are shown through the conventional artificial horizon, the compass
rose, and the speed and altitude tapes, respectively. The tunnel geometry shows
TOTAL ENERGY-BASED FLIGHT-PATH DISPLAY 215
FIGURE 4 The AH for the energy constraints on the task of manually controlling the aircraft
symmetric motion.
the desired path (and thus the altitude profile), whereas a flight-path vector
(FPV) symbol depicts the direction of the aircraft motion with respect to this
path. Hence, when stated in terms of energy, the tunnel geometry shows the po-
tential energy profile, and the FPV shows the actual potential energy rate.
The next two sections describe in detail how the tunnel display can be aug-
mented with information about energy and energy rate through, respectively, the
TERP and the energy angle. Including these two elements in the basic tunnel, as
shown in Figure 5b, yields five important new cues for pilots to perceive and act on
the aircraft energy state: (a) the total energy deviation, (b) the kinetic energy devia-
tion, (c) a preview of the future nominal total energy state, (d) the total energy rate,
and (e) the kinetic energy rate (i.e., the acceleration along the path). In the follow-
216 AMELINK, MULDER, VAN PAASSEN, FLACH
FIGURE 5 Definition of the various ele-
ments and symbols found in a generic tun-
nel-in-the-sky display (a) and the
energy-augmented tunnel display (b). In the
basic tunnel, the following numbers indi-
cate: (1) aircraft symbol, (2) horizon line,
(3) tunnel geometry, (4) speed tape, (5) alti-
tude tape, (6) heading tape, (7) FPV symbol.
In the energy-augmented tunnel display, the
numbers indicate: (8) the total energy refer-
ence profile (TERP), (9) energy angle sym-
bol, and (10) speed marks.
ing sections these five cues are described in detail. Then we discuss how the cues
lead to the appropriate control actions.
Expressing Energy in a Visual Format
The concept of the energy-augmented tunnel display is based on predetermined
speed and altitude profiles that define the nominal approach trajectory. To visu-
ally express energy it needs to be transformed into measures compatible with the
tunnel display. A pilot is not very interested in the absolute energy level of the
aircraft, but rather in the energy deviations with respect to a target. This way the
pilot can use the correction of energy deviations as the means for achieving the
altitude and speed goals. Substituting for the aircraft mass the aircraft weight us-
ing the relation: W=mg, Equations 5 and 6 give the expression for the potential
energy deviation and the kinetic energy deviation:
∆Epot =W∆h, (5)
(6)
with W,g, and Vas introduced previously, ∆hthe altitude deviation with respect
to the altitude profile as depicted by the tunnel: ∆h=h–h
ref; and ∆Vthe speed
deviation with respect to the speed profile: ∆V=V–V
ref. The reader should note
that the potential energy deviation is thus defined positive when the aircraft is
flying higher than the reference height. The kinetic energy deviation is defined
positive when the aircraft is flying faster than the reference velocity. The sum of
Equations 5 and 6 is the total energy deviation:
∆E=∆Epot +∆Ekin. (7)
In the tunnel display the potential energy deviation is already present in the form of
height; it is the aircraft vertical deviation from the tunnel centerline. In this respect,
the tunnel serves as a commanded potential energy profile. Then, through express-
ing the kinetic energy deviation relative to this height the energy representation can
be completed (Figure 6). This is accomplished by dividing Equations 5 and 6 by the
aircraft weight W, yielding the kinetic energy deviation height:
(8)
and the total energy deviation height:
TOTAL ENERGY-BASED FLIGHT-PATH DISPLAY 217
11
(– )( ) (2 ),
22
kin ref ref ref
WW
EVVVV VVV
gg
∆= + = ∆ +∆
(2 )
1,
2
kin
ref
kin
E
VV
E
hV
Wg
+∆
∆
∆= =∆
(9)
When the approach trajectory is defined by an altitude and speed profile, the po-
tential, kinetic, and total energy profiles are now implied. Figure 6 illustrates
how the energy relations are represented using the aircraft position, the tunnel
centerline, and the TERP, which is constructed by subtracting the kinetic energy
deviation height from the commanded height (the tunnel centerline height href).
Figure 7 illustrates the relations among the aircraft, the tunnel trajectory, and
the TERP, according to the energy state matrix of Figure 2. The center picture
shows the desired situation where the aircraft is flying along the tunnel center-
line at the right speed. Some important properties can be noticed. First, the air-
craft height above the tunnel centerline represents the positive potential energy
error; the aircraft height below the tunnel centerline represents the negative po-
tential energy error. When the aircraft is aligned with the tunnel, the potential
energy error is zero. Second, the aircraft height above the TERP represents the
positive total energy error; the aircraft height below the TERP represents the
negative total energy error. When the aircraft is aligned with the TERP, the error
in total energy is zero. Third, the vertical separation between the tunnel center-
line and the TERP represents the error in kinetic energy: When the TERP moves
below the tunnel centerline, the aircraft is flying too fast, and when the TERP
218 AMELINK, MULDER, VAN PAASSEN, FLACH
FIGURE 6 The total energy reference profile (TERP) is based the concept of expressing en-
ergy deviations in height. In this figure, the aircraft is flying above the tunnel centerline (high: ∆h
>0,∆Epot > 0), indicating the positive potential energy deviation. It has a speed that is higher than
the reference speed (fast: ∆V>0,∆Ekin > 0); that is, a positive kinetic energy deviation as re-
flected by the fact that the TERP has moved below the tunnel centerline. The vertical distance
between the aircraft and the TERP indicates the total energy deviation.
(2 )
1.
2
+∆
∆∆
∆= =∆+ =∆+∆ ref
kin
E
VV
EE
hh hV
WW g
moves above the tunnel centerline, the aircraft is flying too slowly. Note that
this property is independent of the position of the aircraft relative to the tunnel.
Again, similar to Figure 2, Line A shows the situation where the total energy er-
ror is zero (the aircraft is aligned with the TERP) but there can be an energy dis-
tribution error (so the pilot can exchange energies to get to the desired energy
state, through the elevator).
Visual Design
The challenge for designing the visual display was to configure the representa-
tion of the TERP with the three-dimensional tunnel display. This was accom-
plished by using linear perspective relations associated with presenting the
TERP as an energy surface that emerges parallel to the nominal trajectory. In
Figure 8a a top-down view on the geometrical design of the TERP representa-
tion is shown. Lines (i) are the inner path lines, which coincide with the tunnel
sides. Lines (ii) are added texture marks that coincide with the lateral position of
the tunnel frames. These marks are expected to help the pilot judge the vertical
TOTAL ENERGY-BASED FLIGHT-PATH DISPLAY 219
FIGURE 7 The energy state matrix of Figure 2, now defined with respect to the reference po-
tential and kinetic energy states, indicating how the relative positions of the aircraft, the tunnel
centerline (dashed lines), and the TERP (thick gray lines), reflect the energy deviations.
distance between the tunnel and the TERP (for the perception of the speed devi-
ation). Lines (iii) are the outer path lines and basically connect the endpoints of
the texture marks to make it a more cohesive representation.
This representation is defined to visually imply a surface while using only the
space outside of the tunnel to avoid clutter in the center of the display. Figure 8b
shows the TERP as shown on the perspective display, clearly illustrating that when
the aircraft is high on energy, the TERP is below the aircraft (below the view-
point); when the aircraft is low on energy the TERP is viewed from below (the
TERP has moved above the viewpoint); and when the aircraft has a zero total en-
ergy error, the TERP is perfectly aligned with the aircraft and its projection on the
display reduces to a line.
Perceiving the Energy Cues From the Energy-Augmented
Tunnel Display
The surface analogy is a fundamental property of the energy-augmented tunnel
display. In a comprehensive study, Mulder (1999, 2003) showed that surfaces
220 AMELINK, MULDER, VAN PAASSEN, FLACH
FIGURE 8 The visual design of the TERP. The top figure shows a God’s-eye view on the
TERP. The bottom figures show how the TERP geometry changes when projected on a perspec-
tive display when the aircraft is flying either above (left), below (right), or in alignment with the
TERP (middle). Wtis the tunnel width.
play a crucial role in understanding the way pilots perceive the aircraft locomo-
tion state from the three-dimensional tunnel geometry motion perspective. Mo-
tion relative to a surface yields an optical expansion pattern that contains very
useful information about the observer’s motion (Flach, Hagen, & Larish, 1992;
Gibson, 1950, 1979/1986): the texture gradients. Visualizing energy through a
surface, the TERP, aims at enabling pilots to directly perceive the aircraft energy
state through the texture gradients resulting from the aircraft motion relative to
the energy surface (Amelink, 2002).
Potential energy.
The aircraft potential energy deviation is represented by
the common splay and density texture gradients that emerge when the tunnel geom-
etry changes due to changes in the vertical aircraft position relative to the tunnel
centerline (Mulder, 1999, 2003).
Total energy deviation.
The total energy deviation is the first new cue that
emerges from the energy-augmented tunnel display. With the surface metaphor,
the total energy error is represented as a virtual eye position relative to the energy
surface. Figure 9 shows the tunnel display augmented with the TERP for the same
conditions as in Figure 7. When there is zero total energy error, the diagonal A-A in
Figure 9, the eye is at the surface level and the edges become parallel with the hori-
zon. When there is positive total energy error, the top-right drawings, then the eye is
above the energy surface and the edges splay out below the horizon. As the total en-
ergy error increases, the edges become more and more splayed away from the hori-
zon (in a way that is similar to the edges of a roadway beneath an aircraft). When
there is a negative total energy error, the bottom-left drawings, the eye is below the
energy surface and the edges splay out above the horizon (in a way similar to tiles
on the ceiling). The total energy deviation is the sum of the potential energy devia-
tion and the kinetic energy deviation (Equation 7), and these are represented by the
position of the aircraft and the TERP relative to the tunnel, respectively.
Kinetic energy deviation.
This is our second new cue. The aircraft speed
deviation ∆Vis represented by the vertical separation between the tunnel and the
TERP. This distance, the kinetic energy deviation expressed in height, is the cue for
speed deviations, independent of the aircraft position relative to the tunnel. When
the speed is right, the total energy error equals the potential energy error and the air-
craft height above the tunnel centerline equals the height above the TERP. This is il-
lustrated in the drawings on the center column in Figures 7 and 9. Due to this prop-
erty, the allowable speed deviations with respect to the reference speed profile can
be projected on the tunnel sides through the speed tick marks, reflecting the fact that
speed deviations are visualized through the vertical separation between the TERP
and the tunnel centerline (Figure 9).
TOTAL ENERGY-BASED FLIGHT-PATH DISPLAY 221
Preview of the Future Required Energy State
An important aspect of the energy-augmented tunnel display is that it provides a
preview of the future commanded energy state, our third new cue. The pilot can
actually see if the stabilized condition will take the aircraft to the commanded
current or future energy states, which should yield a much better anticipation.
The other advantage of a preview is that the pilot can see a commanded change
of path or speed well in advance. Figure 10 shows two types of changes that can
be encountered. A required speed change, as Figure 10a shows, can be recog-
nized by the upcoming vertical separation of the tunnel and the TERP. A
flight-path change can be recognized by an equivalent change of TERP and tun-
nel shown in Figure 10b. As these changes can also take place simultaneously,
the display still shows the pilot a valid energy representation.
When the aircraft energy state is not correct, or, equivalently, when its altitude
and speed do not match the reference profiles, the pilot needs to manipulate the
222 AMELINK, MULDER, VAN PAASSEN, FLACH
FIGURE 9 The energy state matrix of Figure 2 (and Figure 7), now shown including the
three-dimensional TERP surface (defined in Figure 8) into the perspective tunnel display.
controls that are available to control the total energy (throttle) and the energy dis-
tribution (elevator). Then, when changing the total, potential, and kinetic energies,
it is mandatory to have an indication of the energy rates. The mapping of energy
rate on the display is the subject of the next section.
DISPLAY MAPPING: ENERGY RATE
Expressing Energy Rate in a Visual Format
After identifying the energy deviations, a pilot is concerned with correcting
them using elevator and throttle, controlling the energy rates. At this stage, en-
ergy rates are the means to correct any energy level deviations (i.e., short-term
control). Note that the potential energy rate is already present in the tun-
nel-in-the-sky display, as it is depicted by the position of the FPV symbol with
respect to the horizon line. The vertical flight-path angle γis referred to as the
aircraft-specific nondimensional potential energy rate (Lambregts, 1983). Simi-
larly, the total energy rate can be expressed in the total energy angle γE(in the
following referred to as the energy angle):
(10)
TOTAL ENERGY-BASED FLIGHT-PATH DISPLAY 223
FIGURE 10 The energy-augmented tunnel-in-the-sky display provides the pilot with a pre-
view of (a) a commanded deceleration, and (b) a commanded descent. The preview is the third
new cue conveyed by the energy-augmented display.
sin sin .
Esn
V
Eg
γ= = γ+
In this equation, is the aircraft-specific nondimensional total energy rate and
is the aircraft acceleration along the flight path. For small flight angles γthe
following approximation is valid:
(11)
This relation expresses all energy rates in angles, which makes it compatible
with the tunnel display. As discussed further later, showing the energy angle in
conjunction with the already present FPV symbol reveals the three energy rates
to the pilot. The energy angle is also known as the potential flight path; that is,
the flight-path angle that will maintain the existing airspeed based on the current
thrust and drag (Brockhaus, 1994). Showing the potential flight path is common
for HUDs, particularly in the landing phase (Newman, 1995), and has been ap-
plied before in a perspective format (Theunissen & Rademaker, 2000).
Visual Design
The way in which the flight angles are represented by symbols in the display is illus-
trated in Figure 11. The vertical distances between the symbols and the horizon rep-
resent the angles: The aircraft pitch attitude θis the distance between the fixed air-
craft symbol and the horizon. The distance between the horizon and the FPV
indicates the flight path γ. The distance between the energy-angle symbol and the ho-
rizon indicates the potential flight path γE. The form of the latter symbol is a long hor-
izontal line with a gap in the middle, to prevent overlap with FPV. Because the en-
ergy angle does not have meaning in the lateral plane the line is always parallel to the
224 AMELINK, MULDER, VAN PAASSEN, FLACH
FIGURE 11 The display symbols representing the aircraft attitude, flight path, and energy an-
gles. In this figure, the flight-path vector symbol is below the horizon, indicating a descent (γis
negative: decrease of potential energy); the total energy angle symbol is also below the horizon, in-
dicating a reduction of total energy (γEis negative). The flight-path vector symbol is positioned
above the total energy angle symbol, indicating a deceleration (decrease in kinetic energy).
.
E
V
g
γ=γ+
sn
E
V
horizon and the gap is always aligned with the FPV. As becomes clear later, the line
needs to be long to have an overlap with the TERP.
Perceiving the Energy-Rate Cues From
the Energy-Augmented Tunnel Display
Potential energy rate.
The potential energy rate is in fact shown by the FPV
symbol, a very common representation in artificial horizon displays. When the FPV
is aimed below (or above) the horizon, the aircraft descends (or climbs) and the po-
tential energy decreases (or increases). When the FPV is put on the horizon line, the
potential energy remains constant. When the FPV is aimed at the vanishing point of
the tunnel, the potential energy rate equals the potential energy rate as required by the
nominal trajectory.
Total energy rate.
The fourth new cue presented in the energy-augmented
tunnel display is the total energy rate, which can be expressed in the energy angle γE,
defined relative to the horizon. When the energy angle is above the horizon there is
a total energy increase; when it is below the horizon there is a total energy decrease.
Because the throttle is the total energy valve, the total energy angle can be moved
up and down using the throttle. The energy angle also represents the energy flight
path to the TERP. This is illustrated in Figure 12: When there is an overlap between
the horizontal lines of the energy angle symbol and the TERP, the total energy is
converging to the commanded total energy level. The point along the TERP where
it is intersected by the energy angle symbol is the point where the aircraft intersects
the TERP for the given throttle setting.
Kinetic energy rate.
The fifth and last new cue is the kinetic energy rate cue.
Figure 12 illustrates that the energy angle γEis the sum of the vertical flight-path angle
γand the nondimensional acceleration (Equation 11). Thus, the difference be-
tween the energy angle and the FPV expresses the acceleration along the flight path.
Figure 13 shows that when the FPV symbol is below the energy angle symbol the air-
craft accelerates ( ), when it is above the energy angle symbol the aircraft
decelerates ( ), and when both symbols are aligned the speed remains con-
stant ( ). Note that one can accelerate along the flight path with the elevator
control by putting the FPV symbol below the energy angle, and also with the throttle
control, by putting the energy angle above the FPV. Similarly, to decelerate along the
flight path the same opportunities exist. It is clear that this cue is important for finding
and maintaining a steady flight condition: The aircraft establishes a constant speed
only when the FPV and the energy angle symbols are aligned.
The energy angle is also known as the potential flight path; that is, it shows the
vertical flight-path angle that the current throttle setting could sustain at the current
TOTAL ENERGY-BASED FLIGHT-PATH DISPLAY 225
/Vg
/0Vg>
/0Vg<
/0Vg=
226226226
FIGURE 12 The intersection of the energy angle symbol and the TERP in the display indi-
cates the point of interception (Point A) of the TERP in the future. The energy anlge symbol
shows the total energy rate.
FIGURE 13 The difference between the energy angle symbol and the flight-lath vector sym-
bol represents the acceleration along the flight path. This is the fifth and final new cue, presenting
the kinetic energy rate.
FIGURE 14 The relative position of the energy angle symbol and the tunnel geometry indi-
cates the throttle setting for a steady flight path. In a stationary flight (b), the flight-path vector
symbol but also the energy anlge symbol must be aligned with the tunnel geometry, otherwise
the aircraft will accelerate (a) or decelerate (c) because the throttle setting is too high or too low,
respectively.
speed (Newman, 1995). When stabilized (i.e., a constant speed), the energy angle
symbol, like the FPV, has to match the direction of the future tunnel trajectory, as
illustrated in Figure 14b. Hence, it directly links the throttle setting to the com-
manded flight path: It lets the pilot set the throttle independent of the momentary
flight-path angle and speed in a very direct way.
WORKING WITH THE CUES
In the previous two sections we showed that the energy-augmented tun-
nel-in-the-sky display, including the TERP and the energy angle, contains five im-
portant new cues for the manual control task. The cues show energy deviations and
the means to correct them. The throttle, through the engine dynamics, controls the
energy angle γE, and the elevator, through the aircraft dynamics, controls the vertical
flight path γ. In other words, the energy angle symbol and the FPV symbol can be ma-
nipulated with the throttle and the elevator, respectively.
How the cues are exactly used during flight can only be evaluated experimen-
tally. However, the following can be said based on discussions with experienced
pilots and the analysis of the task (Amelink et al., 2003b). The task of piloting can
be split into long-term control and short-term control. The short-term control is
concerned with the immediate response of the aircraft used to correct deviations
and to follow the flight path and speed profile. The long-term control is what pilots
call stabilizing. It is concerned with balancing the forces that act on the aircraft so
that it will naturally fly at the commanded speed and vertical flight-path angle in
steady state. The cues in the display present information to the pilot that facilitates
both parts of the control task.
Short-Term Control
For short-term control the deviation from the commanded energy state should be
directly perceived. The aircraft vertical position relative to the tunnel centerline
is the cue for the potential energy deviation. In the same way, the aircraft verti-
cal position relative to the TERP represents the aircraft total energy deviation.
Now, there are four possibilities, considering the aircraft to be in steady state
each time. First, the aircraft is on the tunnel centerline and on the TERP. This
represents the commanded energy state and there is no need for corrections. Sec-
ond, the aircraft is on the tunnel centerline but not on the TERP. In this case
there is not a potential energy error and the kinetic energy deviation equals the
total energy deviation. To correct the total energy error the pilot must use the
throttle. Third, the aircraft is on the TERP but not on the tunnel centerline. There
is not a total energy deviation but an energy distribution deviation. The kinetic
and potential energy deviations are equal but opposite. Elevator control should
be used to correct the deviation. Fourth, the aircraft is on neither the tunnel cen-
TOTAL ENERGY-BASED FLIGHT-PATH DISPLAY 227
terline nor the TERP. Both total energy and energy distribution deviations occur.
Both throttle and elevator are needed to correct the deviations.
In all cases, the pilot uses feedback from the energy angle symbol and the FPV
symbol to control the energy rates with throttle and elevator. They show the angles
at which the TERP and tunnel will be intercepted, respectively, allowing pilots to
precisely select the control inputs to correct the deviations and to trim the energy
rates for the long-term control.
Long-Term Control
Matching the energy rates to the commanded flight path and speed is the key to
stabilizing the aircraft. When stabilizing, the energy angle is used in conjunction
with the tunnel to determine the stabilized throttle setting; the energy angle
should be aligned with the future tunnel center (as in Figure 14b). To obtain a
stabilized, stationary flight along the tunnel, the FPV symbol as well as the en-
ergy angle symbol should be aligned with the tunnel geometry. This correlates
with the acceleration cue shown in Figure 13b; speed is constant, thus the accel-
eration along the flight path, , is zero.
By showing the total energy angle symbol in relation to the tunnel geometry, pi-
lots obtain a clear insight into what throttle setting is needed to bring the aircraft
into a stationary flight condition along the tunnel centerline. Hence, the pilot heu-
ristic mentioned earlier, where pilots fix the throttle to a certain setting and then
control the approach with elevator only, is very likely to be replaced by (many)
new rules for setting the throttle. Furthermore, pilots will obtain a good under-
standing of why these rules work.
EID-RELATED PROPERTIES OF THE DISPLAY
EID (Vicente & Rasmussen, 1992) is a theoretical framework for designing in-
terfaces for complex human–machine systems. It is the approach to interface de-
sign that gives priority to the worker’s environment, concentrating on how the
environment imposes constraints on the worker. It is based on the three levels of
the skills, rules, and knowledge (SRK) taxonomy (Rasmussen, 1986). A display
based on the EID principles should support the operator on all three levels of
cognitive processing. How the three levels are supported in the energy display is
discussed next.
Skill-based behavior is based on time–space signals that can be directly used
for control. The five cues previously discussed all represent signals, and they are
all compatible with skill-based behavior. This can be illustrated by the following:
When a hypothetical pilot is completely unaware of the energy constraints, he or
she should be able to fly the approach by just keeping the energy angle on the
228 AMELINK, MULDER, VAN PAASSEN, FLACH
/Vg
TERP with the throttle and the FPV symbol inside the tunnel with the elevator.
This is a skill-based tracking task with a low cognitive load.
Rule-based behavior is based on the perception of signs in the work domain that
trigger a set of previously stored rules for dealing with a familiar situation. The two
expected changes are speed and glide slope changes (Figure 10). Because the per-
spective trajectory gives a preview of the future commanded energy state, the pilot
should be able to recognize, without reasoning, which of the changes is coming up
and act on it directly. Also, the tunnel size and the markers on the tunnel wall for
the TERP reference height, combined with the ego position in the tunnel and the
TERP height, provide the pilot signs about acceptable performance. It is very
likely that with the energy display new rules will emerge to replace the existing pi-
lot heuristics and control strategies of throttle-to-path, elevator-to-speed and the
like. Also, pilots will learn quickly how the relations between TERP and tunnel
(Figure 9, reflecting the energy matrix of Figure 2) relate to elevator and throttle
settings, resulting in new behavioral patterns as a result of the new rules. In other
words, pilots will recognize the various energy deviations and develop cognitive
short-cuts to efficiently and effectively deal with them.
Knowledge-based behavior is based on the perception of symbols that carry
meaningful information in the work domain used for unanticipated situations and
problem-solving activities. The visualization of the energy constraints is based on
the top three levels of the AH and should allow for reasoning and problem solving.
The visualization does not tell the pilot what to do, but it shows the structure of the
energy constraints revealing possible solutions. The pilot is allowed to choose any
control strategy that satisfies the system goals. This results in a naturalness of con-
trol that is not available from interfaces based on a more conventional, procedural
task analysis.
It is also possible that the energy display could serve well as a teaching tool, to
explain to pilots how the energy balance works, how it governs the aircraft vertical
motion, and how the available elevator and throttle controls can be used effectively
to achieve the goals. In this way, pilots will get a much deeper understanding of
what is really happening and why certain strategies work.
FINAL REMARKS
The derived AH is a representation of the energy constraints as a subset of the
complete aviation work domain. It can serve as an externalized mental model
that an experienced pilot has for the symmetric aircraft control. As Vicente and
Rasmussen (1992) stated, the AH can only represent what the designer, re-
searcher, or expert knows. It has not come up with answers about the energy
constraints that were unknown, but the AH framework has helped to structure
the process of analyzing the control task. It enabled us to ask the right questions
TOTAL ENERGY-BASED FLIGHT-PATH DISPLAY 229
about the work domain and structure it in a psychologically relevant way that
supports the mapping of goal-directed behavior.
The next step was the actual design of a display to present the energy informa-
tion to the pilot. The AH is part of the EID framework (Vicente, 2002) applied to
the design of the energy display. The energy display is the result of a comprehen-
sive study of the energy constraints in flight using the AH and EID principles
(Amelink, 2002). Whether the contributions of the EID design are beneficial in
terms of the common metrics like pilot performance, workload, and situation
awareness is unclear. Our initial subjective evaluation with professional pilots,
however, looks promising. Initially, pilots found the displays to be rather complex.
This comment was not unexpected. An ecological interface must capture the requi-
site variety of the domain, so when the domain is complex this will be reflected in
the interface. To quote Tufte (1990), “to clarify: add detail” (p. 37). With experi-
ence, however, pilots learned to see and use the energy constraints and the final
comments were very positive.
Research is underway to investigate the energy-augmented display through an
extensive pilot-in-the-loop evaluation. We hypothesize that whereas performance
levels may well be unaffected by the display, the whole nature of the activity will
change significantly, and that the display will allow pilots to explore other control
strategies, increasing their flexibility in the kinds of approaches they may conduct.
In particular the use of the throttle will change. The current heuristic of setting the
throttle before the approach and continuing to control the landing with elevator re-
flects the fact that pilots because they do not see what the throttle does, simply lock
out this degree of freedom. With the energy display, a much more frequent use of the
throttle is expected because pilots can now directly see how the throttle setting is re-
lated to the speed and altitude goals, enabling them to use their controls in a truly co-
ordinated fashion. Empirical evaluations of the display will include dependent
measures that index the amount of coupling across levels of the SRK taxonomy and
AH, along the line of thought advocated in Yu, Lau, Vicente, and Carter (2002).
Another direction that we are currently investigating is to consider other con-
texts in which pilot energy awareness might be particularly important, such as
landings under wind shear conditions where large shifts in energy might occur,
and tasks such as terrain following, where pilots have to operate their vehicle near
the edges of the energy envelope.
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Manuscript First Received: May 2004
TOTAL ENERGY-BASED FLIGHT-PATH DISPLAY 231