1
A SIMULATION STUDY OF TIME-CONTROLLED AIRCRAFT NAVIGATION
BY
Charles Joseph Corley
B.S.E.E. UNITED STATES AIR FORCE ACADEMY
(1968)
SUBMITTED IN PARTIAL FULFILLMENT
OF THE
REQUIREMENTS
DEGREE
OF MASTER OF SCIENCE
FOR THE
IN ELECTRICAL ENGINEERING
at
the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
December,
FP-6 rttr
F
Signature
1974
14_7
of Author
Department of Electrica
Engineerikg,
December,
1974
Certified by
/
Accepted
~
Supervisor
y
artmental
Chairman-Graduate Committee
ARCHIVES
3U42 5D1975
t~anR
R1v-
2
A SIMULATION STUDY OF TIME-CONTROLLED AIRCRAFT NAVIGATION
by
Charles
Joseph Corley
Submitted to the Department of Electrical Engineering on
December 18, 1974 in partial fulfillment of the requirements
for the Degree of Master of Science in Electrical Engineering.
ABSTRACT
A technique has been developed, simulated, and tested
which assists an aircraft pilot in navigating along threedimensional routes and in complying with times of arrival
This technique
specified by air traffic control agencies.
utilizes an on-board computer to determine the airspeeds required to arrive on time and the descent rates required to
In this
maintain the specified routes in the vertical plane.
closed-loop system, the pilot determines the control inputs
required to match his measured airspeed to a computer-controlled bug on the airspeed indicator; the required descent
rate is shown as a bug on the vertical velocity indicator.
The computer requires the aircraft's position in three dimensions, current true airspeed, present time, and the assigned
route-time profile to compute command airspeed and command
descent rate.
The navigation system was tested by professional pilots
in a cockpit mockup of a Boeing 707 interfaced with an Adage
An aircraft simulation which accurAGT-30 digital computer.
ately models a Boeing 707-320B over the full operating range
of airspeeds and altitudes was developed specifically for
The accuracy of the time
these tests and is described here.
of arrival at an initial approach fix was measured for a
linear descent of three degrees from cruise altitude to 10,000
Tests were conducted under zero wind conditions and the
feet.
airspeed at the initial approach fix was constrained to 250
The resulting error in arrival times, chosen from the
knots.
achievable times, had a mean of +19 seconds and a
of
range
about the mean error of 5 seconds.
deviation
standard
THESIS
SUPERVISOR:
TITLE:
Assistant
Alan A.
Professor
Willsky
of
Electrical Engineering
3
FOREWORD
NEVER JUDGE THE HEIGHT OF A MOUNTAIN UNTIL YOU HAVE
REACHED THE TOP; THEN YOU WILL SEE HOW SMALL IT WAS.
DAG HAMMERSKJOLD
A word
of explanation...
in
the
as
a documented
appendix were
mulation.
any
air
that
The
assembly
tion,
is
of
this
luated
cient
few
their
to
Caryn,
and
the
a valuable
without
of
the
adequate
have
counsel
encouragement.
Mr.
and
Bud
invaluable
Vietor of
important,
Christopher who
for
shown
documenta-
American
Mark
Con-
Airlines
insight
all
eva-
into effi-
supervised
my sincere
make
assisted
guidance and organi-
Professor Alan Willsky
but most
tool
si-
researchers.
people who
Captain
and
aircraft
the
engineer, provided
last,
to serve
however, experience has
successive
the
the
appreciation
sacrifices
and
rewards.
This work was supported
reement,
itself
but
language
aircraft model and provided much
And
Linda,
assembly
has proven
study;
add bulk,
contained
acknowledge
flight management.
thesis.
reap
to
support.
the
the
to
language programming,
effort by
zational
control
like
nelly, project
to
aircraft
small value
I would
computer programs
included, not
reference to
traffic
the
under
DOT-FA71 WAI-242, between
Federal Aviation
Task
the
F of
United
Administration.
an
interagency ag-
States
Air
Force
4
TABLE OF CONTENTS
page
ABSTRACT
.
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FOREWORD
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TABLE
OF CONTENTS
LIST
OF
FIGURES
LIST
OF
TABLES
CHAPTER
I
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INTRODUCTION
2
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7
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11
12
16
1.1 STRATEGIC CONTROL......
1.1.1 THE DESCENT PROFILE
1.1.2 ASSIGNMENT OF ARRIVAL TIMES
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20
1.3 THE NAVIGATION CONTROLLER .
21
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24
1.2 THE NAVIGATION CONCEPT
1.4 THE AIRCRAFT
CHAPTER II
8
SIMULATION .
THE AIRCRAFT MODEL
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29
30
30
30
30
2.1.3 VEHICLE AXES
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2.1.4 EARTH AXES
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33
2.3 THE AERODYNAMIC ANGLES
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33
2.4 EQUATIONS OF MOTION
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.43
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38
39
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46
2.1 REFERENCE FRAMES
2.1.1
2.1.2
2.2
WIND
BODY
AXES
AXES
THE EULER ANGLES
.
.
.
.
.
2.5 AERODYNAMIC FORCES
. . . .
2.5.1 LIFT
. . . .
2.5.2 DRAG
.
2.5.3 SIDE FORCE
2.6 AERODYNAMIC
2.6.1 ROLL
2.6.2 PITCH
2.6.3 YAW .
MOMENTS
. . . .
. . . .
. . . .
2.7 THE ENGINE MODEL
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47
47
48
49
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51
5
page
CHAPTER III
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60
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60
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62
. . . . . . . . .
3.3 AIRSPEED CALCULATIONS
3.3.1 INDICATED AIRSPEED . . . . . . . .
3.3.2 COCKPIT MACH INDICATION
. . . . .
63
63
65
. . . . . . . . . . .
70
THE ATMOSPHERE MODEL
3.1 DENSITY
3.2 SPEED OF SOUND
CHAPTER IV
THE NAVIGATION
CONCEPT
.
72
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.
76
78
79
83
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.
85
86
. . . . . . . . . . . .
87
. . . . . . .
5.1 AIRCRAFT MODEL EVALUATION
.....
5.1.1 DECELERATION PERFORMANCE
. . . . . . . .
5.1.2 CLIMB PERFORMANCE
88
89
91
5.2 TIME-CONTROLLED NAVIGATION EVALUATION.
5.2.1 TEST RESULTS . . . . . . . . . . .
. . . . . . . .
5.2.2 ACCURACY ACHIEVED
5.2.3 FAILURE TO OPTIMIZE FLEXIBILITY. .
94
99
100
101
ACCOMPLISHMENTS, RECOMMENDATIONS,
AND CONCLUSION . . . . . . . . . . . . . . .
104
. . . . . . . . . . . .
6.1 RECOMMENDATIONS
6.2 CONCLUSION . . . . . . . . . . . . . . .
107
108
. . . . . .
110
4.1 THE VERTICAL NAVIGATION CONTROLLER
.
.
4.2 TIME-CONTROLLED NAVIGATION . . . . . .
4.2.1 FEEDBACK CONTROL . . . . . . . .
4.2.2 COMPUTATION OF EPTA AND LPTA . .
4.2.3 AVERAGE AIRSPEED DURING DESCENT.
4.2.4 COMPUTATION OF COMMANDED
AIRSPEED . . . . . . . . . . . .
. .
4.2.5 EFFECT OF WIND DISTURBANCES
CHAPTER V
CHAPTER VI
EXPERIMENTAL RESULTS
APPENDIX A
THE AIRCRAFT SIMULATION PROGRAM
APPENDIX B
THE FOUR-DIMENSIONAL NAVIGATION PROBLEM
REFERENCES
.
.
157
173
6
LIST OF FIGURES
.
.
AIRCRAFT VELOCITY PROFILE .
NORMAL DELAY SPREAD . . . .
. . .
OPTIMUM DELAY SPREAD
.
.
.
PROFILE
.
.
.
.
.
1-1
1-2
1-3
1-4
1-5
DESCENT
2-1
2-2
2-3
2-4
2-5
2-6
2-7
2-8
2-9
2-10
2-11
2-12
. . . . .
WIND AND BODY AXES
VEHICLE AXES AND EULER ANGLES
. .
NOTATION FOR BODY AXES
HIGH SPEED LIFT COEFFICIENT
LOW SPEED LIFT COEFFICIENT
3-1
3-2
3-3
3-4
DENSITY AND
SIMULATOR COCKPIT
.
.
SEA LEVEL
THRUST
.
.
.
.
.
.
.
.
.
COEFFICIENT
.
.
.
LOW SPEED DRAG POLAR
HIGH SPEED DRAG POLAR
PITCHING MOMENT
.
.
.
.
.
.
14
18
22
22
25
31
32
34
40
42
44
45
50
52
56
57
59
MAXIMUM THRUST VARIATION
IDLE
THRUST VARIATION
.
.
THRUST RELATED TO THROTTLE POSITION
.
.
.
SPEED-OF-SOUND RATIOS
61
66
67
69
.
MACH TO CALIBRATED AIRSPEED CONVERSION
BOEING 707 AIRSPEED/MACH INDICATOR
. . . . . .
SIMULATOR INSTRUMENT PANEL
4-1
4-2
4-3
4-4
VERTICAL
5-1
MAP OF ROUTES FLOWN
NAVIGATION CONTROLLER
. . . . . .
TIME DIFFERENCES
.
CONTROLLER
TIMED NAVIGATION
.
.
707-320B
VELOCITY PROFILE
.
*
.
TIME HISTORY
5-2
DELAY SPREAD
A-1
FUNCTION SWITCH ASSIGNMENT
.
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73
77
73
80
96
103
. . .. .. .
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113
7
LIST OF TABLES
page
ROUTE-TIME PROFILE
. . . . . . . . . . ..
.
19
1-1
SAMPLE
2-1
2-2
2-3
2-4
AIRCRAFT PERFORMANCE DATA . .
.
AIRCRAFT IN THE 707 FAMILY . . .
CONTROL DEFLECTIONS 707-320B
.
NORMAL OPERATING RANGE . . . . .
. .
. .
. . .
. .
28
28
41
53
5-1
5-2
5-3
DECELERATION CAPABILITY RESULTS . . . . . . . . . .
SIMULATOR CLIMB PERFORMANCE . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . .
TEST RESULTS
90
93
97
A-1
ANTICIPATED MAXIMUM CONTROL VALUES
. . . . . . . .
116
.. . . . . . .
. . .
-. . .
. . . . . . .
. . . . . . .
8
CHAPTER I
INTRODUCTION
control
The
is
responsibility of
the
Since
increasing numbers
One
in
changes
revolutionary
increased
offers
flicting
craft
permit
any
in
strategic
and
space
arrivals
airport
permit
of arrival at
times
waypoints,
safer
space and
-
airport
to
at
be
control
in the
the
scheduled
can
at
and more efficient
lower
to
a sequence
fourth
runway
of
the
ground.
and
dimension
the
a saturation
(4D)
aircraft[l]
strategic
several
other
three-dimensional
-
ultimate
time.
between airThis
would
"bottleneck" at
a maximum rate.
utilization of
aircraft operating expenses
in-
aircraft non-con-
each
of
these
attained without
achieve separation
system of heading and/or speed changes
on
reach
to
controlling
capacity
By assigning
important advantages.
recent years
cannot be
ever-
flow of
four-dimensional
as
States
United
tasked with pro-
been
airports
major
the methods
known
proposed concept,
control,
Within
increased capacity
condition where
the
and expeditious
of aircraft.
caused several
have
creases
has
it
1930's,
the
in
Aviation Administration.
Federal
the
orderly,
safe,
the
for
viding
in
inception
its
operating
traffic
air
of
It would
available
than
also
air-
the present
sent from a controller
9
While
here, must
all
ling
pilot
assignment of a "route-time profile", as
the
of necessity be done by
a controversy
arrivals,
ground facility controlover
exists
role of
the
a totally centralized management concept
with an automatic monitoring system on the ground
aberration and issue
traffic
control process
and advocate that he be provided
correct
for deviations from
The Boeing Aircraft Company adopted
in which they
ter position in a recent study[2]
time assignment algorithm for use by
report
any
pilot should participate in the
an on-board capability to sense and
the 4D schedule.
to detect
Those favoring "distributed
corrections.
management" believe that the
This
the
in the execution of this schedule.
The FAA favors
air
described
the lat-
develop a route-
the controlling agency.
states:
"The pilot has the responsibility to maintain
adherence to a detailed route-time profile and has
with airborne equipment to make this
an airplane
acts in a
controller
traffic
The air
possible.
surveillance and advisory capacity when the pilot
maintains conformance to the route-time profile
and has the equipment necessary to quickly generate new route-time profiles for airplanes, re[2: p.3]
scheduling them when necessary".
To aid the pilot
in discharging this responsibility, an
on-board navigation method has been designed, simulated,
tested
Systems
This
at M.I.T. on the simulation
Laboratory
technique
assists
and
the
Flight
the
pilot
facilities of the Electronic
Transportation
in
and
Laboratory.
complying with assigned
10
times
of arrival
at three-dimensional waypoints.
jective was incorporated into
commanded
that
the event
that
the aircraft's
time.
This
flexibility was
that the controlling
considered
agency had to
majority of
this
appeared that both
a
objectives had
At the last minute, new evidence revealed that
present approach is
-
only suitable
task which it performs
for navigating
admirably.
concept of optimizing flexibility is
the discussion is
to
sional air routes
tem of
Nevertheless,
the
final design,
considered worthwhile and
and assigning times of
and beyond.
for the air traffic
Irrespective of
the requirements
control sys-
the source of
are universal;
the route and
capabilities of
each aircraft and must not conflict with the routes and
to other aircraft.
since it is undeniably
however,
dimen-
arrival at intermediate
times assigned must be within the performance
assigned
the
retained here.
a logical candidate
the 1980's
the
the assigned
The precise control of aircraft by specifying three
points is
aircraft.
and the preparation of the
concept
report, it
later
desirable in
reschedule
testing of this
time
the airspeeds
capacity to arrive earlier or
Through the
been met.
second ob-
for meeting the assigned time at a waypoint would al-
so maximize
than
the design so
A
The latter aspect is
a responsibility of the
times
ignored here
controlling agency;
the relationship between aircraft performances and
route-time profile is
central to
the
on-board navigation
the
concept.
11
Therefore in
the remainder of this
assignment will be discussed
chapter,
and the
and
tion
The
concept
are discussed,
is
explained,
a logical extension of
the models
for the aircraft
the implementation of the naviga-
and
the
test
results
are
summarized.
computer programs for the aircraft model and navigation con-
troller
are
tion
1.1
In succeeding chapters,
atmosphere
time
on-board navigation concept
designed and tested here will appear as
these ideas.
the route and
of
contained
their
in
component
the Appendix along with
a brief
explana-
parts.
STRATEGIC CONTROL
While
licable to
the generalized concept of strategic control
any phase
of flight
discussion most often
tude
into the
centers
terminal area.
from departure
on
the descent
It is
this
to
is app-
landing,
the
from cruise alti-
descent phase,
and par-
ticularly the descent to congested airports, where the greatest
benefits are
Under
rive
foreseen.
the present system of radar vectoring,
randomly at the boundaries of
the terminal area
within approximately 40 nautical miles
be sequenced and spaced
speed
when
commands.
These
for landing by
performance
aircraft
to possible
(airspace
of the airport)
and must
a series of heading and/or
"path stretching" maneuvers
performed at low altitudes
aircraft ar-
and prolong
are costly
the exposure of high
collision with lighter aircraft
12
operating
in the same airspace.
aircraft may be asked to "hold"
tern until
In extreme cases,
by flying
arriving
in a racetrack pat-
they can be assured separation from other aircraft
in the landing stream.
Strategic control, on
arrivals
the other hand, would "derandomize"
in the terminal area by assigning
an "initial approach fix"
area boundary.
(IAF) or waypoint on the terminal
Aircraft would
then adjust
descent from cruise altitude to
Aircraft entering
separated
way.
at the
times of arrival at
speed during
arrive at the assigned time.
same IAF would fly a common path
in time) and proceed in an orderly stream to
Aircraft
the
from other
IAFs would assume
(but
the run-
their position in
the stream by merging with the common path at an intermediate
waypoint and at a non-conflicting
The ability
of arrival
to adjust speed while descending
times
that an aircraft can achieve by
alone are functions of
times
and the range
speed control
the route geometry chosen and
aircraft performance limits.
fied before
time.
Because
can be calculated,
the route must
individual
be speci-
the descent profile to be
flown must be chosen first.
1.1.1
to
THE DESCENT PROFILE
The etymology of many
terms unique
aviation has been lost, but descent profile at least
logical basis.
the descent
The three-dimensional route to be
to the terminal area can be plotted as
has a
flown during
a function
13
of altitude and distance Here
1-1.
or
-
in profile
as
shown in Figure
the path in the horizontal plane is assumed to
sist of straight-line segments with each turning point
fied
as
an
additional
The Boeing
con-
identi-
four-dimensional waypoint.
study points out
that "airplane performance is
probably the single most important criterion in
the design of
the
The available
terminal
area descent
drag, minimum thrust,
mit the angle
due
to
profile".
and weight of
(y) at which it
gravity.
[2:
p.
63]
the aircraft combine to li-
can descend without
The rate of descent
accelerating
(dh/dt) required to main-
tain that angle is a function of speed and is limited by
Boeing, with
bin repressurization schedule.
ledge of
current jet
transports,
feet per nautical mile
300
ft/n.mi. below that altitude
bility of all aircraft.
"clean" airplane
portant
their intimate know-
chose a vertical
gradient of
for descents above 10,000
250
the ca-
feet and
as being well within the
capa-
Although their analysis was based on a
(landing gear and flaps
to the present discussion that
retracted),
it is
im-
they considered spoiler
deployment to be an acceptable method of increasing drag in order to decelerate or to maintain
the clean aircraft drag is
Other proponents
choice
slope when
insufficient.
of linear,
commended other slopes with 300
an oft-quoted
the required descent
[3,4,5].
fixed descent profiles have reft/n.mi. at all
altitudes being
The navigation concept
to be
40-
30
uj
u.J
Lu
20-
2318
FEET/NAUTICAL MILE
10
DECELERATION REGION
318 FEET/NAUTICAL MILE
TH
OM
-
THRESHOLD
OUTER MARKER
TF
IAF
-
TURN FIX
INITIAL APPROACH FIX
-EF
-
ENTRY FIX
SL
0
EF
TF IAF
TH OM
25
50
75
100
125
DISTANCE FROM THRESHOLD (NAUTICAL MILES)
Fig. 1-1
Descent Profile
150
175
15
described here
(Y= 3 0).
slope
vary
was
uses
testing with values other
level flight
ft/n.mi.
than 318
to facilitate
segment at 10,000 feet shown
transition
found a 10 nautical mile level
for present day
ded a 15 mile segment
mance
318
to
in the simulator cockpit
ft/n.mi.
[2].
purposes
The
of
Using
in Figure 1-1
from high-speed descent to
speed below 250 knots as required by
quate
a
undertaken.
The
exists
restricted to)
Provision was made
the slope but
not
(but is not
flight
the FAA.
The Boeing
segment
commercial transports,
a
study
to be just adeand they recommen-
to insure reliable
deceleration perfor-
fifteen mile segment was
also adopted for the
this study.
this descent
now be specified.
profile,
the strategic control
It is described by the
route
can
geographical position
(in some
convenient coordinate system) of each waypoint and the
altitude
required
actual
route
direction of
at
that point
chosen would depend
flight
to maintain
upon an
and would have
the profile.
individual
to include,
The
aircraft's
as a minimum, the
following points:
1.
The entry fix where strategic control commences.
This point is fixed so that the
assignment algorithm can compute times over
a known distance.
2.
The initial approach fix where aircraft join
the common path to the runway.
16
At this
3. The outer marker of the runway.
point aircraft must adjust speed and assume the proper configuration for landing.
4.
The runway threshold.
5. Any turning points
line segments.
required between straight
6. Additional points as required, particularly
along the common path to insure that time
separation is maintained.
Having
specified the route of
to specify appropriate times
terize
flight,
of arrival
is only necessary
completely charac-
the route-time profile.
To increase airport
1.1.2 ASSIGNMENT OF ARRIVAL TIMES
all
to
it
times assigned must be based on
the runway threshold.
queried prior to the
roach airspeed
the desired arrival time at
the Boeing
design, aircraft would be
entry fix as to
their expected final app-
In
(which varies with landing weight
pheric conditions)
in order
to relate
and atmos-
runway arrival times
the arrival time required at the outer market.
are assumed to fly a common airspeed along
this is used to
capacity,
to
The aircraft
the common path and
compute required arrival time at
the initial
approach fix.
To
separate and sequence several aircraft arriving simul-
taneously,
there must be a range of arrival
aircraft can achieve.
This range
times which each
is bounded on
the lower
side
17
This is the
by the earliest possible time of arrival (EPTA).
time the aircraft would arrive
mum airspeed,
if it accelerated to its maxi-
flew the prescribed route at that maximum, and
then decelerated to
comply with any
the assigned waypoint.
The
time of arrival
is
(LPTA),
airspeed constraints at
upper bound, or latest possible
achieved by
minimum speed, and then accelerating
point
constraints, if any.
flight-times is
The
often called
decelerating,
flying at
to comply with the end-
difference between the two
the "delay spread" available, and
the relative position of the assigned time of arrival
ween these bounds is
bility".
a measure of
the aircraft's
EPTA has no flexibility with respect
have
"time flexi-
arrive
For example, an aircraft assigned to
assigned.
The maximum true airspeed that an aircraft can
available
feet, by
10,000
also a function of altitude and
g maneuver without buffeting
aircraft velocity profile is
[2].
shown
The conflict
in order
is
usually
can perform
a
A general view of an
in Figure 1-2.
gic control scheduling algorithm would store
aircraft type
The
FAA directives.
defined as the airspeed at which the aircraft
1.3
fly varies
defined by structural limits, by maximum
thrust, or below
minimum airspeed is
at the
to arriving sooner but may
great flexibility in arriving later than
with altitude and is
(ATA) bet-
The
strate-
this data for each
to compute EPTA and LPTA
for each arrival.
detection function would then sequence the aircraft
18
CABIN PRESSURE LIMIT'
.;t-:TRUTLII
I MU
.......................
/
.
..~......................
STANDA RDDAY
40
...*
..........................
e........ ....
....
ese ...
. .
. .
...
......
..............
F LGH
-
-
30
21....
5
..
..
.. ..............................
IE GC)
............................................
. ................
.................................
. .. .... .... ...
Mt I
U
. . ...................
0~.............
............
...
....
25
00.......
MACH NUMBER
.........
***00000
0 00* 90 .........
.
o..............
300..
354
cm
... .(..TsTRo
Fig.1-2
Moo*.0
.. . VEL- CI y.0.
50
450
0
*$ vo.,% .
A..
I..~
sPEED)
Aircraft Velocity Profile
imp"!
19
and
assign a unique route-time profile
the time
to each aircraft with
at the initial approach fix within the bounds of EPTA
and LPTA.
(A sample route time profile --
gests sending via data-link to
the pilot
such as Boeing sug--
shown in Table
is
1-1.)
Distance
Index
number
Altitude
(feet)
(nautical mHes)
Gon
Groud
(knots)
lc
oto
Clock
Control
(seconds)
indicator
1 (entry fix)
1
32,681
0
455
18
32,681
27,340
22.000
16.000
10,000
39
61
82
106
130
423
427
432
392
356
340
521
700
910
1141
0
0
0
0
0
7
8
9
10
11
12
10,000
10.000
4,800
2,400
1,600
1
0
140
145
161
16
172
177
267
273
238
185
179
131
1253
1326
1541
1685
1757
2 (initial approach fix)
3 (turn fix)
4 (merge fix)
5 (final approach fix)
6 (outer-marker)
7 (thrshold)
2
3
4
5
6
Table 1-1
The
from entry
Sample Route-Time Profile
flexibility inherent in this
later than the assigned
1877
capacity to arrive earlier or
time suggests a navigation concept which
not only complies with the assigned time, but
some sense
this
flexibility.
also optimizes
in
20
1.2
THE
NAVIGATION
determined
order
not
sample
the
In
route-time
a-priori
at
a
constant
cated
airspeed
or
cause
of wind,
temperature,
These
relationships
it
possible to
is
cations
by
culation
the
using
for
ror
took
not
a
the
and
are
airspeed
if
winds
only
the route-time profile.
offers
the
This
as
could
groundspeed
3.
cockpit indi-
the
an iterative
done
could be
of
forecast
current
or
it
by
an
airspeed,
to
requirement.
2.
A feedback control system allowing continuous corrections to schedule.
3.
Continued operation
system failure.
4.
A reduction in controller workload by making the pilot an active participant in air
traffic control.
of
or
er-
is
on-board
Reduced communications
event
on
pilot
1.
the
cal-
speed-up
advantages:
in
be-
Nevertheless,
Shifting the responsibility
following
an indi-
at
atmosphere.
performed
position,
in
does
pilot
the other hand,
On
be
required
flies
a series
from
different
aircraft
the
performing
schedules.
and
he
airspeed to
off schedule.
complex calculation
of
in Chapter
and
is
from
differs
aircraft
to the
aircraft
computer knowing
craft
required
that
fact,
density
discussed
forecast winds
commands
In
Boeing has
1-1,
However, the
time.
that
schedule
Table
schedule
groundspeed.
relate
ground and sent
slow-down
groundspeed
Mach
trial
of
profile
the assigned
comply with
to
fly
an
CONCEPT
ground
and
the air-
21
While an on-board navigation system was contemplated by
Boeing,
the method of
implementation was not specified
Collins
Radio Company has
[2].
conducted tests of a four-dimension-
al navigation computer which performs the
iterative selection
of an appropriate airspeed schedule
However, the concept
to be described
[4].
here uses a modified approach to
the computa-
tion and arrives at an airspeed schedule which incorporates
flexibility in an innovative way.
1.3 THE NAVIGATION CONTROLLER
spread available on any descent profile decreases
The delay
monotonically with descreasing distance to
is
the waypoint.
(Variations of maximum
shown schematically in Figure 1-3.
and minimum airspeed with altitude would determine
for purposes of
and LPTA would
wind,
illustration.)
Under perfect conditions the EPTA
converge to the assigned time as
the waypoint.
the aircraft
In the presence of disturbances
pilot error, or inaccuracies
a perfect controller has
the aircraft can
than it
should ATC be forced to
point it
earlier.
the ATA.
time, but note that,
this particular example,
rival time.
such as
In
computed an airspeed sche-
dule such that the aircraft arrives on
can be advanced,
ap-
in observing position and speed,
the delay spread may converge to a value other than
Figure 1-3,
the actual
the values shown in Figure 1-3 decrease linearly
delay spread;
proaches
This
For example, at a distance of
could arrive 3 minutes later,
always be
in
delayed more
change the ar-
50 miles
from the way-
but only one half minute
Let us hypothesize an example in which this would be
22
TIME
44g
OP
DEL AY
SPREAD
- ATA+3
49 !4t
ASSIGNED TIME OF ARRIVAL
=
dn
OF ARRIVAL
TIME
EARLIEST POSSIBLE
100
25
50
75
DISTANCE TO WAYPOINT (MILES)
Fig. 1-3
- ATA+2
- ATA +1
ATA
ATA- ATA-1
- ATA- 2
0
Normal Delay Spread
TIME
ATA+3
ATA+2
-ATA+1
ATA
-----------------
100
EPTA
ATA- ATA-1
INCREASED FLEXIBILITY
- ATA-2
25
50
75
DISTANCE TO WAYPOINT (MILES)
Fig. 1-4
Optimum Delay Spread
0
23
undesirable.
Suppose
two aircraft, A and
B,
are 50 miles
from the
tial approach fix
(on separate route-time profiles).
A
arrive one minute
is
scheduled to
rors in the wind forecast,
the delay
is
going
prior to B,
to be
Aircraft
due to
time far enough to occupy A's
easily delay one minute and
time slot
to A.
If no gaps
arrivals,
air traffic
relinquish its
control is
now faced with
re-scheduling
succeeding aircraft to arrive one minute later and
way
arrival time originally assigned to A goes unused.
Several alternatives appear in
avoided
forces all aircraft
net
operating costs.
to fly
scheduling algorithm because it
longer than necessary and increases
Instead,
they strive to
this
cient cruise and descent time of
arrival.
second alternative would be
schedule
corresponds to
to the EPTA, traffic permitting;
The
the mid-
Boeing has logically
delay spreads.
this approach in their
the run-
this hypothetical situation.
choose the ATA for each aircraft near
their respective
own
are available in the sequence of
all
point of
advance
assigned time slot.
It can, however,
The first is to
er-
Aircraft B has
It is unable to
spread shown in Figure 1-3.
its arrival
late.
but
ini-
to
closer
an effi-
fly an airspeed sche-
dule which equalizes the flexibility on either side of the ATA.
This
is depicted in Figure 1-4.
here and
a sub-optimum control
This
is
the approach adopted
law was developed and
tested for
24
the no-wind
ly since
cable
1.4
case.
It will be argued,
at least heuristical-
tests were not completed, that
this approach is appli-
in the presence of unknown winds.
THE AIRCRAFT SIMULATION
A consortium of three M.I.T. laboratories
nics
--
the Electro-
Systems Laboratory, Flight Transportation Laboratory and
the Man-Vehicle Laboratory -tor resembling a Boeing 707.
been used
for several years
have a fixed-base cockpit simula(see Figure
to
study
borne Traffic Situation Display to
tem.[6]
While this
device has
minal and
enroute environment,
1-5)
The cockpit has
of an Air-
the applications
the air traffic
potential uses
control sys-
in both the ter-
its applications have been studied
exclusively in the near-terminal area at low altitude.
reason the aircraft
dynamics were simplified and are
resentative of a general
range
of
area.*
this
only rep-
large jet transport over the narrow
airspeeds and altitudes required for
Its
For
the near-terminal
performance was woefully inadequate for
the range of
airspeeds and altitudes contemplated for time-controlled navigation.
It thus was necessary to
create an accurate aircraft
model which would provide representative performance for the contemplated studies.
* A more accurate model has since been developed [7] but again
it is only valid in the lower altitudes of the terminal area.
I
PO
Fig.1-5 Simulator Cockpit
26
The aerodynamic data required for full simulation is
closely held by individual aircraft manufacturers.
less,
a model
of a Boeing
Neverthe-
707-320B with Pratt and Whitney
JT3D-1 turbofan engines has been developed from data obtained,
deduced or derived
model
development represents
effort and
air
from various
aircraft
a major part of this research
the results are now available
traffic control research as well as
navigation studies.
This
sources.*
The model
for other advanced
the current
is discussed
time
in detail in the
following chapter.
*Link Division of General Precision, Inc., American Airlines,
the U.S. Air Force, Pratt and Whitney Aircraft, the Dept. of
Aeronautics and Astronautics at M.I.T. and a Boeing publication, Jet Transport Performance Methods [8], each contributed
pieces which, when combined, provided most of the important
aerodynamic parameters.
27
CHAPTER II
THE AIRCRAFT MODEL
There are many similarities among jet transport aircraft
manufactured today because
function -
similar
passengers
fast,
and cargo.
they are
all designed to perform a
efficient, and
economical
While configurations
ferrying of
and intended uses
may dictate varied landing speeds and maximum ranges,
the op-
erating airspeed range and cruising altitudes for many types
aircraft are
2-1 is
As
an illustration
a sampling of aircraft operating
the Boeing
that
quite similar.
the
Company study
[2].
of this,
limits as
The conclusion
airspeed flexibility which will be
of
Table
contained in
to be
drawn is
required for
controlled navigation could be found in any modern jet
time-
trans-
port.
The
due to
Boeing 707-320B was selected for modeling primarily
the availability of aerodynamic data.
However, it
an advanced member of the Boeing 707 family and is widely
for intercontinental and transcontinental routes.
shows
that
a total of 862 Boeing 707's
these, 167 bear
707's
but
the designation
(-320s, -320Cs,
different engines
not all of
airlines,
-420s)
707-320B but
there are
used
2-2
Of
409 more
that have the same wing structure,
related aircraft are
the number might be
transports owned by
have been built.
or fuselage configurations
the 707-320B or
Table
is
compared with the
domestic air carriers -
[9].
While
flown by U.S.
total number of
approximately 2500 -
28
TABLE
2-1
AIRCRAFT PERFORMANCE DATA*
MIN.SPEED(KTAS)
AIRCRAFT TYPE
ALTITUDE
AT MAX.WEIGHT
707
10,000
21,600
10,000
24,000
10,000
22, 500
10,000
22,000
10,000
25,000
10,000
22,000
229
275
231
304
243
295
255
315
262
330
200
240
727
737
747
DC-10
720-B
*SOURCE:
[2 pp. 212-213]
TABLE 2-2
AIRCRAFT IN THE 707
TYPE
707-120
-120B
-220
-320
-320B
-320C
-420
KC-135 & OTHERS
TOTAL
*SOURCE:
[9]
FAMILY*
NUMBER
20
121
5
90
167
283
36
140
862
MAX. SPEED (KTAS)
AT MAX.WEIGHT
435
527
452
530
407
495
436
532
430
526
420
530
29
to show that data for a Boeing 707-320B is
applicable
to
a
significant percentage of the aircraft in use today.
In this
chapter,
are presented.
from numerous
dynamic
the equations governing aircraft motion
The derivation
references
(see for example,
forces and moments
but the terms
is standard and is
ted specifically
to
from the sources
listed in Chapter 1.
tions
[10,11]).
calculations
as
available
Boeing 707-320B by
they bear on the validity of
is
the data obtained
Therefore,
the assump-
the model.
an important parameter and is
The
in
thrust
discussed along
with the relationship between thrust and throttle
position.
REFERENCE FRAMES
Four reference frames
known as the "flat
is
aero-
are rela-
and linearizations based on that data are discussed
detail
2.1
The
are based on a standard derivation,
and values used in their
the
available
generally
1.
are used here in what
earth" approximation.
valid under the
This
is
commonly
simplification
following conditions:
The earth's rotation is small compared to
the rotation of the vehicle. (o, =7 x 10-5
rad/sec which is smaller than any vehicle
rotation
of interest.)
2. Vehicle velocity does not exceed Mach 3.0
(Certainly true for subsonic transports.)
3.
The vehicle is a rigid body. (Certainly
not true, in fact, but aeroelastic effects
are unlikely to influence the results
of
the present study.)
30
2.1.1
The wind axes system in a right-handed, ortho-
WIND AXES
the aircraft
gonal set of vectors with the origin fixed at
ter of gravity.
(and hence opposite
is
important
This
in Figure 2-1.
is depicted
This
tive wind").
coincident with the total
The +x wind axis is
velocity vector of the aircraft
cen-
to the "relaaxes
system
forces acting on the
in computing the aerodynamic
aircraft.
gonal and
The x
axis
in Figure
body
The body axes
BODY AXES
2.1.2
also right-handed
is
2-1.
fixed along
The z axis
the fuselage reference line as shown
is
"downward"
taken as a plane of
rotated into
VEHICLE AXES
gonal
The aerodynamic
the body axes from the wind axes and
The vehicle
for-
all
frame.
frame is a right-handed, ortho-
reference system with origin at
vity.
and the x-z plane in the
symmetry.
forces and moments are computed in this
2.1.3
and ortho-
center of gravity.
have their origin at the aircraft
frame is
ces are
are
The x-y plane is parallel to
the aircraft center of
our "flat"
gra-
earth with the +x
axis pointing to magnetic north
(assuming a fixed magnetic decli-
0
nation of approximately 15 W).
The z vehicle axis is
with the gravity vector as
2.1.4
ted for
EARTH AXES
shown in Figure
coincident
2-2.
The earth axes reference is arbitrarily loca-
the simulation to
be conducted.
For
the present work, the
31
Fig.2-1
Wind and Body Axes
32
IB
north
-v
-B
-w
g or kv
Fig. 2-2
Vehicle Axes and Euler Angles
33
origin
is
southwest of
Massachusetts,
at
the Logan International Airport, Boston,
approximately 71 0 11'W, 42 0 12'N.
vehicle
axes,
+x
to east because of an anomaly of the
axis
play.
2.2
the +y
Altitude
earth axis points
to magnetic north
the
and the
computer map dis-
above sea level is then positive.
THE EULER ANGLES
Euler angles
are used to designate the orientation of the
body axes system with
respect to the vehicle
axes.
tions
are performed in the conventional order;
about
the z vehicle
0 about
3)
Unlike
2.3
are
"azimuth"
about the
angle;
is
a rotation
2)
9
a rotation
the "elevation" angle
resulting x axis
is
the
"bank" angle.
shown in Figure 2-2.
angles are fundamental in determining the aerodynamic
forces that
lage angle
ao
0-
the
1)
THE AERODYNAMIC ANGLES
Two
gle
is
the now rotated y vehicle axis
a rotation $
These
axis
The rota-
act on the vehicle.
of attack, and
of attack is
used
by a constant
and sideslip
the sideslip
that of the zero lift
in
20,
the lift
the
fuse-
A second an-
line or wing chord plane,
calculations,
angle
angle.
the
but
of incidence.
the
two
differ
The angle
only
of attack
angle rotate the wind axes system into the body
axes
in
Thus
in terms of
gure
2-3,
the
8,
These angles are a,
order
(-83,a,o)
analogously
the body axes
to
the
Euler angles
velocity components
above.
shown in Fi-
0
w
w
w
w
w
U~
w
w
w
Y
X,u"
PL,p
YJ v
.1s-
F2
Fig. 2-3
Notation for Body Axes
35
=
at
tan
-1
w
-
-
f<<
(2-1)
-
ff<r<7r
(2-2)
-1 v21
S
where
2.4
=
V
+ v2
=-p1
V
1
sin
+ w
2
EQUATIONS OF MOTION
The
classic equations of motion from Newtonian mechanics
they
are summarized here as
The
iented as
are written in the body
force equations
locity components
are used in the simulation.
(u,v,w) and angular velocities
The ve-
axes.
(p,q,r) are or-
shown in Figure 2-3
-sin
SAx
+
Ay
M
g
Az
0
cos
Osin
cos
Ocos
i+
0
r
r
o
q
-p
u
-q
o
TRS
v
0
w
0
(2-3)
Ax, Ay
where
forces
and Az are resultant aerodynamic
after
ro-
tation into the body frame.
the body axes
The moment equations are also written in
tem.
sys-
(2-4)
Ixx
o
- Ixz
o
Iyy
o
o
Izz
-Ixz
where L,
M,
and N are
L
q
M
N
the rolling
0
+
-r
q
-p
r
-q
p
moment,
0
Ixx
o
o
0
Iyy
0
Ixz
o
Izz
pitching
-Ixz
moment,
p
q
Lr
and
36
a plane of symmetry thus eliminating all cross
taken as
The equations
of inertia except Ixz.
ducts
neglecting the Ixz p and Ixz r
Ixz is
small
(a
are
pro-
decoupled by
common practice where
the other inertia terms).
compared to
The Euler angle rates
lar
terms
is
that the x-z plane
Note here
yawing moment respectively.
are computed
from body
axes angu-
velocities.
r=
Cos 0
cos
coso
o
-
Since only the
functions
pAt has
n+l
=
cos
n
sin
1n+l
=
sin
1n
increment,
an optimum value of !
The correction
term, s
E =
,
is
cos2
sin$
cosO
q
of
the Euler angles
computations
[12]
sin
+
cos
p is
is
used
cosine of
for the
is illustrated here
-
(2-5)
r
to obtain the sine and
This approach
cos
the time
p
cos$
azi-
is used for pitch and roll.
muth angle and an identical approach
Here At is
sino
Gilbert-Howe algorithm
Euler angle rates
angles.
cose
are required for all
themselves
and displays, the discrete
the Euler
-
cO
sin
sine and cosine
and not the angles
to integrate
sin$ sinO
ipn
n-
n-
At -pAt e
cos
n
(2-6)
n-
At -pAt
sinrn
(2-7)
a constant, and
6
the product
for any At>o.
computed by
2p-l
2-+sin
(2-8)
37
frame
Earth
is
integrating the sum
Vehicle frame ve-
frame velocity and wind velocity.
of vehicle
locity
obtained by
position is
following series of axis
computed by performing the
rotations
Vx
o
1
L:
Vy
1
-sine
o
cosO sinj
cosj
o -sind
Vz
0
c.os
sin
o
u
o
-sin9
cos
o
y
cos6
o
o
1
'w
sin
cose o
o
1
(2-9)
The
are parameters of several
and cosine
their sine
coefficients and
mic
to
aerodynamic angles
rotate the wind axes aerodynamic forces
The
Here
sine
are
and cosine
sin
a
~
cos
a
~
V
as
~ v
cos
1
~ a
frame.
the body
(2-10)
(2-11)
~
(2-12)
2,
(2-13)
approximation is
used to determine
The maximum angle of attack
16 degrees.
At
this point
Sideslip angle,
approximation is
into
follows:
in radians.
than 4%.
used
functions are
V
sin
the small angle
computed
aerodyna-
the
approximation is
, seldom gets
even better.
for the 707
as
is
a
and
about
in error by
large as 160
6
so
less
the
38
as previously mentioned, are
The aerodynamic forces,
tated into
in
the order
( ,a,o).
LiL IL ]L ]
cosa
Ay
o
=
Az
o -sina
cos3
1
sin
o
-sine
o
cos3
o
o
1
cosa~ o
sina~o
-Drag
Side Force
(2-14)
-Lift
AERODYNAMIC FORCES
The previous equations are
applicable to
other atmospheric vehicle' with six degrees of
ject to
the previously stated assumptions.
force and moment equations,
dimensionless aerodynamic
ticular aircraft.
on
coefficients
Since the validity
the accuracy of these
steady
several texts
flight condition.
[e.g 10,11
The
aerodynamic
of the present
are heavily
simulation
dependent
discussed in
In all cases
the
co -
series expansion about a
The derivation is
available in
] and is omitted here in favor of an
explanation of the particular
for modeling.
freedom and sub-
coefficients, they are
are the result of a Taylor
state
aircraft or
associated with a par-
some detail in the following paragraphs.
efficients
any
the other hand, are based on
and its potential in future applications
on
r
the body axes by utilizing the aerodynamic angles
Ax
2.5
ro-
Where possible
terms in the expansion selected
used to
the approximations
the available data are contrasted with that data.
Where
fit
data
was not available or where median values were picked for highly non-linear effects,
the model was
pilots to confirm the values chosen.
model will be discussed in chapter
tested by professional
The final
five.
tests
of the
39
2.5.1
LIFT
All of
mic pressure
the aerodynamic
(1/2pV ),
the dimensionless coefficients,
priate geometric terms
The lift
4pV
C
=
L
2
S
[CL
C
The
(M)a
in this simulation is:
+ CL
66E +
CL
(6F-6
0
-a
)+C L
6F<6 0
0
0
.0143/degree
L 6F-a
and appro-
.0055/degree
CL
6F
dyna-
to satisfy the dimensional requirements.*
equation as implemented
Lift =
forces are products of
6F<6'
=(0
1.081/degree
term CL
(M)
(2-15)
6F>6
6F>6
0
the slope of
is
the
lift
coefficient
curve as
0
a
function of Mach number.
tio of aircraft velocity to
(Mach number is
the local speed of sound.)
ticular approximation used is
CL
=
4.584 -
2.220
the dimensionless
ra-
The par-
a second order polynomial,
- MACH + 5.387
-
(MACH) 2
(2-16)
0
for a
This is
in radians.
plotted in Figure
2-4
along with
the
0
actual curves
for a Boeing 707-320B.
that sample points
It is important to note
for this approximation
(and those that
low) were obtained by iteration of the actual
program.
as well as
Therefore,
it serves
a measure of
as
a check of
assembly language
the program logic
the approximation's accuracy.
WING AREA (S)=
* For the 707-320B:
WING SPAN (b)=145.75 FT; MEAN CHORD
fol-
3010 FT2
(c) = 22.69
FT
LA
a
a
kA
4
_r_
0
Fig.2-4
High Speed Lift Coefficient
41
The CL6F term is an incremental increase in lift
flap
for
deployment.
flap angles
with C
The particular approximation
(SF)
over 6 degrees.
(an addition to the
due to
used is linear
This correction, along
slope
of the
force lift
co-
6 F-a
efficient for flaps
The C
term represents
vator deflection
term and is
over 6 degrees),
(63).
are
shown in Figure
the variation in
2-5.
lift with ele-
This is a relatively small corrective
taken as a constant
.0055/degree.
flection has the sign and maximum magnitude
Elevator de-
shown in Table 2-3.
TABLE 2-3
CONTROL DEFLECTIONS
707-320B
Positive
Control
Elevator
(6e)
Sign Convention
Maximum
Trailing
+250
edge
Rudder
(6R)
Aileron
Spoiler
Flaps
(6A)
(6B)
(6F)
-150
down
Trailing edge
left
yaws
Remarks
+26.50
(Nose
left)
Rt trailing
edge up (Aircraft
rolls
right)
+18+200
inboard Outboard availoutboard able only in
conjunction
with flaps
Positive
deployment
600
Maximum limited with indicated airspeed
Positive
deployment
500
Deploy fully
in 30 seconds
42
2.8
MACH :0
AIRPLANE
RIGID
GEAR UP
2
CL 2.0
1.6
1.2
4
8
12
16
a (DEGREES)
Fig. 2-5
Low Speed Lift Coefficient
20
43
2.5.2
DRAG
Drag
Aircraft drag
pv 2S[ C
=
is modeled by
(M)+k(M)C
the following equation:
+CD
2+AC
min
gear
(6F-60)+C
-6B]
6F
6B
(2-17)
.012
.01233 +
.014
+
.014
+
_
CD
min
(.0524
.063
.063
=
k
ACD
+
+
.0033(H-.8)
.0371(M-.845)
.1455(M-.845)
M<.7
.7<M<.8
.8<M<.845
.845<M
(.2356)(M-.8)
.8333(M-.845)
M<.8
.Z<M<.845
.845<M
.0105
=
gear
CD
0
0
.0026/degree 6F>6 0
6F
CD
=
.00083/degree
2
The
is
common
lift-drag relationship
contained
and
in
This
gures
is
there
quired
for
efficient
changes
good.
.3.
linear
term is
brackets
of
for
2-7
flight.
level
flight
altitude.
.84
The
Over
2-15).
drag at
of
the
For
range
By
varying
this
lift
actual
drag
in
Figure
2-6
and
min
curves is
In both fi-
values which will
at Mach
from about
.7,
.15
the
to
.46
approximation
for
the
speed
coefficients
k.
high
Above
as
.84
range
be
lift
the
too
low Mach
for
range
is
(as
CD
the
of
example
varies
.82 Mach
CDmin
to
shown
can be made
case
Mach where
variation
equation
for high Mach numbers.
only a limited
similar
the
is
CD
+ kCL
min
total lift coefficient
an approximation
approximation
level
in
A
to
CL
and in Figure
numbers
Mach
the
k with Mach,
obtained.
and
The
used here.
CD =
of
result
is very
from
Mach the
of
co-
with
vary between
a
re-
.80
.1
the
inaccura-
1.8 -
1.6 -
C~
1.2
CL
.8
.4 -
0
ACD LANDING GEARz.0105
.04
.08
.12
.16
CD
Fig. 2-6
Low Speed Drag Polar
.20
.24
.28
45
.65
.60
.55 -
.50-
.45 CL
.40
.35 -
.30 -
.25 -
.20
.15 -
.10
.012
I
.014
.018
.022
.026
CD
Fig.2-7
High Speed Drag Polar
.030
.034
46
cies are deemed less
significant
since this is on
of the normal operating range and more
the fringe
accurate values would
require significantly more computation time.
The additional drag due
CD6F term.
to flaps is represented by the
Here an increment proportional
shown
The
drag due to the spoilers, CD 6B,
However, the
is
blowdown effect
is incorporated by limiting maximum spoiler
in the
where KIAS
is
is
max
=(2-18)
of the
spoilers
deflection as
60
KIAS<188 knots
-. 283(KIAS-188)
the indicated airspeed
defined
2.5.3 SIDE FORCE
important
taken as a constant
following equation:
600
6B
speed
effect of this
in Figure 2-6.
.00083/degree.
shown
flap deployment
The
over 60 is added to the drag coefficient.
is
to
KIAS>188 knots
in knots.
(Indicated air-
in Chapter 3.)
The y body axis force was
in this simulation and is
considered less
modeled by the following
simplified equation:
Side Force =
The
2pV S[ C
coefficient due to
-S + C
*6R]
6
6SR
side slip is
(2-19)
taken as a constant -. 917/
radian which is accurate to within approximately 10%
full range of Mach numbers.
The
coefficient
due
over the
to rudder de-
47
approximation of a very non-linear effect
by flight
2.6
and was confirmed
test.
AERODYNAMIC MOMENTS
The aerodynamic
moments determine
and yaw characteristics of
or Mach variation because
the pitch, roll,
studied.
the particular aircraft
are modeled here without
They
correction for non-linearities
the present
concerned with steady state flight
aircraft moments sum to zero.
due
a rough
which is at best
taken as +.004/degree
flection is
simulation is
conditions,
primarily
i.e. when the
Variations in transient effects
to varied Mach numbers or altitude are
therefore omitted
in favor of simplified computation.
The roll equation used is:
ROLL
2.6.1
L
=
2pV
C
Sc[
=
1
CA=
C
-6A+C
- +C 1
S
6A
(2-20)
-p
6R]+4pVSb2C
6R
p
-. 1719/radian
.00113/degree
C
C1
=
C1
=
.0002/degree
-. 38/radian
p
The coefficient
of roll due to ailerons, C1
accurate in this case.
model the
A,
is
the least
Insufficient data was available
inboard aileron,
outboard aileron, and
flection variations which command rolls
in the
to
spoiler de-
707.
The
48
outboard ailerons, which operate
only when
the inboard ailerons were
ployed, and
de-
combined into a single
The value
term (6A).
aileron deflection
the flaps are
for C16A was chosen
to give a reasonable roll rate for a clean aircraft at airspeeds near the midpoint of the normal operating
p
ance to roll and is
inherent
the aircraft's
term represents
The C
accurate to within 35%
range.
resist-
in the
flight en-
C1 R,
is highly
velope.
The roll coefficient
due to the rudder,
non-linear and was finally chosen
from representative values
by trial and error.
The pitching moment
PITCH
2.6.2
is
computed by the follow-
equation:
ing
M
=
o
C
=
Cm
=
C m 6=
C
C
C
a+Cm
+Cm
Sc[C
-pV
a
q
m.
m6 F
-. 955/radian
-. 009/degree
=
-16/radian
=
-3.7/radian
[ Cm +CM. ]-q
a
q
(2-21)
.048
0
m6F =.0033/degree
m
-(6F-14)]+1pVSC
-6E+C
6
6F<14 0
6F>140
49
The basic pitch
coefficient is
a funtion of Mach number, but
for the present study such variations are
result
in level
ferent
from the real aircraft.
flight pitch attitudes
that
However, such effects are
aircraft are usually obtained by repositioning the
flight pitch reference.
plotted
The line determined by C
changes in pitching moment with
,
m6 F
in
m
level
and C
0
m
is
a
in Figure 2-8 for comparison with the pitching moment
coefficient of the actual aircraft at Mach
C
are slightly dif-
the pilot since relative attitudes
rarely noticeable to
the
This may
ignored.
.6.
To simulate
flap deployment,
an increment,
for each degree of flaps over 140.
m
While the actual aircraft uses stabilizer trim rather
than
was
added to C
elevator trim to
of the
preserve the aerodynamic effectiveness
elevator, elevator
trim is used in this
simulation.
This is justified because the sampled control-input voltages
are not subject to
aerodynamic losses and this
approach permits
the elevator to be positioned so that neutral column position
represents level
flight elevator deflection.
and C
terms are combined on the assumption of
m.
q
a
This holds true for the majority of
zero side slip angle.
The C
m
flight operations.
by up
to 32%
While used here
YAW
they increase
at high mach numbers and high altitudes.
effects have been neglected.
2.6. 3
as constants
The yaw equation is:
These
50
-.13
/
-.12
-.10
/
/
0
-.08
1/
Cm
I-.--,
-.06
-. 04
-.02
-2
4
6
8
GFRL (DEGREES)
10
.02
ACTUAL
.04
APPROXIMATION
,A'
Fig. 2-8
Pitching Moment Coefficient
51
N
2
pV Sb
=
C
C
C
Yaw
m
[C
-*+C
m
m
-6R]+4pVSb
6R
(2-22)
-r
r
m 6 R= -. 0011/degree
m
= -. 15/radian
r
forces and moments
and C
C
m
.115/radian
=
like the side force
-
2
are
-
is
less
in the simulation.
accurate to within
34%
than the
important
other
Therefore, while C
and 22%
respectively,
the
m6 R
variation
of Cm
with changes
in angle of
attack have been
r
neglected.
2.7
THE ENGINE MODEL
For time-controlled navigation, it was decided that
the most
significant engine parameters were maximum and mini-
mum thrust.
sures that
Knowing that
these extremes are
the simulated aircraft can
airspeeds and achieve realistic
achievable in-
fly maximum and minimum
acceleration and
deceleration
rates.
The net
thrust of a turbofan engine is
function of many factors.
these
Rather than attempt
a complex
to take all of
factors into consideration, the engine manufacturers
per-
formance data was used to determine maximum and idle thrust
over the altitude
Figure
2-9 shows
and Mach ranges normally flown by the
707.
one such performance graph for sea level.
52
PRATT AND WHITNEY
JT3D-1 TURBOFAN ENGINE
W a = AIRFLOW
20000
16000
Un
12000
II--
w
8000
z
4000
00
0.4
0.2
MACH
Fig. 2-9
0.6
NUMBER
Sea Level Thrust
0.8
1.0
53
The operating boundary considered for each altitude is
in Table 2-4.
At
sea level,
takeoffs were neglected
TABLE
shown
to give
2-4
NORMAL OPERATING RANGE
MAXIMUM MACH 2
MINIMUM MACH'
ALTITUDE
.51
.57
.63
.71
.79
.88
.88
.88
.88
.17
.17
.33
.37
.42
.47
.53
.61
.75
Sea Level
5000
10000
15000
20000
25000
30000
35000
40000
1 Vref or initial buffet
for 1.3g maneuver
2 Indicated airspeed structural limit converted
to Mach below 25000ft. Mach limit above 25000.
to Mach
a range of Mach
.17
from Figure 2-9
that it is
thrust variation with Mach.
.51.
can see
relatively easy to approximate the
The inspection of similar charts
for other altitudes lead to the
imating the variation of
Over this range one
following equation for approx-
the thrust extremes with altitude and
Mach:
T(h,M)=T(h
o
,0)
M+
(h-ho)+
DT
aM h=ho
Mh m=o
To calculate maximum thrust
let
3h3m
(h-ho)-M
m~o
h=ho
(2-23)
54
Maximum Thrust
= T(hM)
(2-24)
following values:
using the
0
0<h<15 ,000 ft.
0
h=( 15 ,000
T(ho,o)
=
13,800
.281
m=o
3T
3M lh=ho
32T
Dh3M m=o
h=ho
h>15,000
ft.
lbs.
lbs/ft
-7800
-3125
lbs/Mach
lbs/Mach
+.312
+.185
lbs/Mach-ft
lbs/Mach-ft
ho=o
ho=15000
ho=o
ho=15000
let
For idle thrust,
(2-25)
Idle Thrust = Max[T(h,M), o]
using
following values:
the
ho
=
0
0<h<15 ,000
ft.
h>15 ,000
ft.
15,000
T (h 0,o)
=
1,000
M m=o
=
0
DM h=ho
=
-2,000
lbs
all
h
lbs/Mach
all
ho
ho=0
D2 T(0
3h3M m=o
h=ho
0
+ 07
lbs/Mach-ft.
ho=15 ,000
55
approximation, the manufac-
this
check the accuracy of
To
turers maximum thrust values versus Mach for
are
dotted
lines
idle thrust values.
In each figure the
represent values obtained from the actual simu-
lation logic over
tude
ranges of interest
the speed
for that alti-
Table 2-4).
(cf.
While
the computed values are very close to the actual
there appears to be
maximum thrust at all altitudes,
error in the idle
thrust approximation shown
it
actual idle thrust data is
no more accurate
extracted from Figure 2-9.
In particular,
of zero idle thrust above
conclusion
.5 Mach
to warrant
2-11.
that the
than what
can be
the unlikely value
in Figure 2-9
that the solid lines of Figure
some
in Figure
is important to note
In examining these curves,
accurate
a similar
Figure 2-11 shows
consolidated in Figure 2-10.
compilation of the
several altitudes
led to the
2-11 were too in-
approximation.
a better
With the two extremes of maximum and idle thrust established
it is
only necessary to relate
intermediate throttle
thrust value.
positions
to a representative
generally
command engine
control.
Engine speed and, hence,
The
speed by regulating the engine
engine speed and thrust are not
flow through the engine
in Figure 2-9)
fuel
throttle position variations
with altitude are small enough to be neglected.
air
throttles
linearly related.
Unfortunately,
However,
(labeled Wa and measured in lbs/sec
may be considered proportional to engine speed
56
15000
ACTUAL
14000
APPROXIMATION
12000-
100000
8000
I
40000
z
40000
40000
2000
I
0
0.2
Fig. 2-10
I
0.6
0.4
MACH NUMBER
i
0.8
Maximum Thrust Variation
1.0
57
1200
-ACTUAL
-- APPROXIMATION
1000
_
0000
Go 800600-f
400-
3400
3
0
f
6000
-j 400
20
0.
09%
0.8
0.9
200 -0
0.2
0.3
0.4
Fig. 2-11
0.5
0.6
MACH NUMBER
0.7
Idle Thrust Variation
58
Then by normalizing the airflow for a given altitude
[13].
and Mach, throttle position can be related to
Poly-
thrust.
on this
nomial approximations of various orders were attempted
basis
the
for a representative altitude and Mach.
In each case
So
coefficient of the second order term dominated.
ease of
computation without significant
loss in pilot
the thrust was equated to throttle position by the
for
"feel"
following
relationship:
Idle
+
Max
=hrust
ThrustThrust
Idle
Throttle)2 0 Throttle <
-PositionPosition
(2-26)
where Idle Thrust
This
and
2-25.
70%
RPM yields
actual
al
tests.
to engine
and Max Thrust are defined by equations
relationship obeys
50%
thrust
old cockpit adage
found quite
and was
that.
acceptable in
Using the assumption that airflow is proportionspeed and engine speed to throttle position, the
thrust data of Figure 2-9
the solid
an
2-24
is
related to
curve in Figure 2-12.
throttle position by
Equation 2-26 is
the same figure as a dashed curve.
depicted in
59
14000
-12000
=-MAX
z
10000r 80000.
c 16000
6ACTUAL
rx
4000 -
BASED
ON AIRFLOW/
APPROXIMATION
z
W 2000 o
IDLE
0.0
IDLE
Fig.2-12
0.2
0.4
0.6
0.8
1.0
FULL
NORMALIZED THROTTLE POSITION
Thrust Related to Throttle Position
60
CHAPTER III
THE ATMOSPHERE MODEL
of
The variations
aircraft
density
of
are
terms
(p)
This
temperature.
a
factor
in
all
Many
Mach number which
of
functions
is
simulation
very
much above
and moments.
forces
aerodynamic
atmosphere are
for altitudes
simulations
atmospheric
the
of
5000
the
in
feet.
The
calculations
the
individual
varies with
performed
is
important
ambient
entirely under
the
*
assumption
of
the
tions
used
to
approximate
sound
are
in
outlined
indications,
ables,
standard
because
are also
atmosphere
ICAO
of
variations
this
functions
The
density and
The cockpit
chapter.
are
they
[14].
of
equa-
speed
of
airspeed
atmospheric
vari-
explained here.
DENSITY
3.1
The
ratio
of
local
to
density
sea
density
level
(P
)
P0
in
the
standard
atmosphere
actual relationship
P
(1
P0
h
-
(from [11])
as
can
shown
be
in
Figure
expressed
=
temperature
R
=
universal
m
=
equivalent
International
Congress
The
(3-1)
0O
altitude
3-1.
as
Mg1
-)cR
=
where
varies
lapse
gas
rate
constant
molecular weight
of Aeronautical
for
air
Organizations
61
a 00.6
o
.e
0
10,000
20,000
30,000
40,000
ALTITUDE(h) FEET
Fig. 3-1
Density and Speed of Sound Ratios
50,000
62
g
= acceleration of gravity
T
=
sea level temperature
sea level density (.002378
P9 =
For
fast real-time simulation, it
this
the
precise equation and
is more
slugs/cu.ft.)
efficient to
avoid
instead to approximate the curve by
following polynomial:
1 -
-
1.835
(h/65536) +
1.0
(h/65536) 2
(3-2)
P0
where
65536 is a power of
stant.
2 (216)
used as a normalization con-
This approximation does not
cause below 40,000 feet
appear in
Figure 3-1 be-
the approximation lies precisely on
the actual curve.
SPEED OF SOUND
3.2
Mach number
air
speed
as
of
(from
a/a
where
defined
to the ambient
true velocity
local
is
sound to
sea
as
the ratio
speed of
level
sound.
speed
of
the aircraft's
The ratio of
sound varies,
in
[11])
-
o-h
h<36,089
i/XgR VT 0-(36,089) h>36,089
X =
adiabatic constant for air
a =
sea level speed of sound
Because temperature remains
standard atmosphere,
Once again
of
constant
(1116.4
ft.
ft.
ft/sec)
above 36,089
the speed of sound is
(3-3)
feet in the
constant as well.
this function was approximated in order
to
increase
63
the
speed of computation.
1 a/a
=
The
relationship chosen was:
ft.
ft.
h<36,089
h>36,089
(3.683x10-6 )-h
.867
(3-4)
The actual curve and the approximation are indistinguishable
3-1.
in Figure
AIRSPEED CALCULATIONS
3.3
3.3.1
INDICATED AIRSPEED
Because
of atmospheric variations
several airspeeds besides
there are
city relative to the air) and Mach that
The
airspeed read
(IAS) and
in the cockpit is
proportional to
is
airspeed
true
(true velo-
are used in aviation.
termed indicated airspeed
the dynamic pressure caused by
the aircraft's forward velocity [8].
But
to measure the dyna-
mic pressure, the ambient static pressure must be subtracted
error
due
(position error)
involved
in determining
to
static pressure
to the disturbed airflow around the aircraft.
is measured experimentally for each aircraft
correct
(CAS).
neglected so
mously.
that calibrated
Because it
1%
This error
type and is
the indicated airspeed to a calibrated
However, the error seldom exceeds
and
and indicated are
some
There is
from the total pressure at the airspeed sensor.
used
airspeed
is usually
used synony-
is proportional to dynamic pressure, calireference to the pilot in
brated airspeed is
an invaluable
avoiding a stall.
The constant of proportionality is
chosen
64
so that calibrated airspeed and true airspeed
are equal at
sea level.
If the atmosphere were
incompressible and,
constant density, calibrated airspeed and true
always be
that
forward velocity increases,
airspeed reading must be
(EAS)
airspeed would
However, the true nature of air
as the aircraft's
brated
speed
equal.
hence had a
by a suitable
requires
the cali-
corrected to equivalent
compressibility factor.
air-
And then,
because the proportionality constant was valid only at sea
level
the equivalent airspeed
variations
of equation 3-1
equation for
true airspeed
TAS =
is
corrected
or 3-2 to find
true airspeed.
EAS//p/p
requires a cockpit
The
is
(3-5)
An accurate simulation over a wide
thus
for the density
range of altitudes
readout of calibrated
assuming no position error) airspeed
(or indicated
rather than true airspeed.
The non-linear nature of the compressibility
correction makes
it more desirable to relate calibrated airspeed to Mach by an
approximation of the precise equation
M 2 =5
where
(
M
=
6
= P/P
VC
=
Mach
1+0.2(661.5
2
3.5-
(from [8]):
+1)0.2861]
(3-6)
number
= pressure
ratio in standard atmosphere
calibrated airspeed in knots
65
This
function is plotted in Figure
3-2 and
the following
equation was derived by inspection:
VC
-(h)
V
-C
M
where
M
h=o
+
d(
)
h
dh
(3-7)
C
M
h=o
d(VC )
d
dh
- 656 knots/Mach
.0091 knots/Mach-ft
=
This approximation is
shown as the
3.3.2 COCKPIT MACH INDICATION
dotted lines in Figure 3-2.
Besides indicated
airspeed,
the pilot
uses a Mach indicator at high altitude to maintain
efficient
cruise conditions.
A combination
indicated airspeed
and Mach meter as employed in the Boeing 707
ure
3-3.
Note
that the Mach indicator has
rotates with altitude changes
indicated
airspeed.
relationship
indicator
fixed
By the
tion is
a fixed scale which
to align with the corresponding
The linearized Mach-to-indicated-airspeed
for the present
simulation.
is proportional
.7 Mach and 300 knots
on the
shown in Fig-
of Equation 3-6 was used to create a similar Mach
of the Mach scale
between
is
The angular rotation
to the difference
indicated.
face of the display at
The 300 knots
that the
.7 Mach indica-
at the 9 o'clock position at approximately
.7
VC
- -
300 =
is
the nine o'clock position.
following formula one can see
Mach Angle =
in knots
159.2-
.0064-h
26,000
feet.
(3-8)
66
4P4)
.9
/-
.8 -,
/
2I
.5-
/APPROXIMA
-
---- ACTUAL VAL UE
--TION
.3
.2
I
,.1
100
200
Fig. 3-2
I
I
500
400
300
CALIBRATED AIRSPEED VC (KNOTS)
Mach to Calibrated Airspeed Conversion
600
67
MACH -INDICATOR
Fig. 3-3
Boeing 707 Airspeed/Mach Indicator
68
where
is
M
defined by Equation 3-7.
shown in the
The displayed airspeed-Mach indicator is
upper left-hand corner of Figure
inherent
There
is some error
in this approach because the airspeed
tween successive Mach graduations
tudes.
3-4.
However, in this respect,
difference be-
is not constant at
it is no
all alti-
different from the
fixed scale employed in the actual aircraft.
I>
ao
Fig. 3-4 Simulator Instrument Panel
70
CHAPTER IV
THE NAVIGATION CONCEPT
The
accurate models
described
in
provide
realistic basis
acy
of
a
any
Chapters
of
the
II and
III were
airplane.
In
developed
and
During
their
tested
feasible
solution.
ployment
was
in
the
pilots
VOR,
quickly
in the
using
separated
DME, RNAV,
in
horizontal
a variety of
*VHF omnirange,
tion equipment,
ly.
by
inertial,
is
the
of
systems
necessary
make
to
at
arrive
testing
the
a
and
assump-
computation-
linearizations
for
the justification
solution
their
em-
the
in
simulation.
three
in four
parts
the vertical
plane
on-board
etc.*
I
described.
assumptions
into
four-
Chapter
to
to
accur-
research are
order
These
The
control
to navigate accurately
horizontal plane,
Navigation
was
developed aircraft
The requirement
sions
in
also but
was demonstrated
independently
it
this
the
capabilities
the navigation
during
development,
presented here
are
chapter
and linearizations
tions
ally
this
in
in order
of
system.
introduced
the performance
on
atmosphere
developed
time-controlled navigation
dependent
and
the measurement
for
dimensional navigation concept
highly
aircraft
is
-
plane,
performed
dimen-
navigating
and
in time.
every
day
navigation equipment
Using
the
cockpit
by
-
simulator
distance measuring equipment, area navigaand inertial navigation equipment respective-
71
in Chapter I,
described
ulate any of
But VOR and DME were judged
common horizontal navigation aids
most
pit
these.
it would have been possible to
controls
for using
to be
simthe
and cock-
and programs
There-
them were already available.
this was the horizontal navigation method used.
fore,
second part of the navigation
Vertical navigation, the
descent profile described in
fixed,
be
may not
to
the linear,
Chapter I.
While this
is relatively simple if restricted
problem,
example,
the most efficient descent for aircraft
[3]
a simple feedback system
for an alternative),
was designed and simulated to assist
this profile.
the pilot
Vertical navigation devices are
available which perform the same function same way quired
in
(see, for
in maintaining
commercially
in the
possibly
but are not widely used because they are not
The particular approach
the present ATC system.
used here will
re-
be described primarily as a reference.
Accurate navigation in time was
the ultimate objective
of this research and, because of the many atmospheric variables
which affect and alter
during climbs and descents,
task.
As explained
sumes that
there is
the flight path,
it was
in Chapter
considered a simple
I, the present approach as-
an advantage attendant to being
arrive at the waypoint
able to
earlier or later than the assigned
time by an equal amount.
An example was formulated in which
one aircraft was asked to arrive
would be late.
not
particularly
earlier because another
Even if the on-board navigation systems
used
72
become so
arrival
the
precise
times,
that all
their assigned
aircraft meet
circumstances will
occasional
arise
reschedule aircraft.
controlling agency will have to
the terminal area, runway
Emergencies, weather in
or blunders might necessitate a schedule change.
circumstances
it
to
this
the time of
its
range of achievable times.
craft will
generally
arrive close
be scheduled
but not at,
late.)
traffic
to not only meet the
-
permitting
to
the earliest possible arrival
the likelihood of being
chapter
in this
Therefore, the design described
assigned time of arrival but
preserve flexibility as it is
will
-
of
the midpoint
is unlikely since air-
This
(Assigning the EPTA increases
time.
seeks
to,
arrive at
scheduled to
arrival without
in one direction
flexibility
aspect loses
or the other unless
these
Under
As was shown in Figure 1-4,
delay.
an airspeed schedule which meets
concern for
changes,
that an aircraft would be
seems as likely
asked to advance as
in which
defined here.
include an intuitive argument
as
The
to
description
to why this may be a
good approach in the presence of unknown winds.
4.1
THE VERTICAL NAVIGATION CONTROLLER
descent profile is shown
pilot
in Figure 4-1.
is shown in the closed loop.
Note here that
This could
a monitor.
In
the
also be the
aircraft autopilot in which case the pilot would
the loop and would act as
fixed
to maintain the
The feedback system designed
be outside
either case,
the
73
DISTURBANCES
3-D ROUTE
Fig. 4-1
Vertical Navigation Controller
DISTURBANCES
3-D ROUTE I
DESIRED AIRSPEED
AT WAYPOINT
Fig. 4-3
Timed Navigation Controller
74
tion
set by the pilot
(8e)
error between his measured descent rate
manded descent rate
requires
computer
(hC) as
to determine h
(h )
and
and
is
the comThe
computer.
the
dimen-
three
(in
position
three-dimensional route
the
The computation
.
by pilots.
often used
(Vm),
pilot
seeks to minimize the
determined by
only aircraft
true airspeed
sions),
The
(or autopilot).
the controller and he
actually part of
posi-
the elevator
the aircraft consists of
control input to
is based on a technique
The technique
consists of making
cor-
to a required altitude at a vertical velocity rate
rections
which will put the aircraft at the altitude in 30 seconds.
changed to 32
This was
seconds
for
ease of
computation and
the following formula was derived:
h
where h
m
(t)
C
=
h P(t+32)-h M(t)
32
32
required
onds of flight.
where
altitude and h
is the current measured
the altitude
h
(4-1)
ft/sec
(t+32)
by the descent
in the
This is calculated
=
(D-d-Vm-32)-tany
after
profile
+
(ft)
d =
15 mile deceleration segment if
= measured true airspeed
y
=
altitude assigned at
=
angle
of descent
sec-
h WP-2)
distance to waypoint
h
32
following manner:
D =
V
(t+32) is
applicable
(ft/sec)
the waypoint
(ft)
(ft)
75
subroutine PROFL in
These computations are performed in the
the
FOURD computer program of Appendix B.
This approach is beset with
It
assumed here.
component of velocity as
the horizontal
true airspeed is not
is always in error
ity vector
and
tangent of 0
by the
the aircraft veloc-
the.angular difference between
where 0 is
The measured
inaccuracies.
this
However,
the horizontal plane.
angle
equals y when the aircraft is on the profile and won't exceed
5*
about
greater
due
to
(9%
error)
corrections.
when making
than about 50
will cause
the effect of gravity
the aircraft
In any
[2].)
(Pitch angles
to
accelerate
case, Vm is not
the
the aircraft groundspeed which would accurately predict
aircraft position after 32
Nevertheless, the posi-
seconds.
tion predicted using instantaneous
airspeed was
true
suffi-
ciently accurate to determine the required altitude, h
for
the tests
conducted here.
Many of
offset by the feedback nature of
that
the inaccuracies
the design and
command descent rate is updated three times
The commanded descents are very stable
easy to maintain the
it is
Wind would probably
for this
area required
the fact
per
second.
reason and
induce a bias in the deviation such
the profile a
to wind speed.
Whether or not winds
would be strong enough to cause deviations
buffer
are
required profile.
that the average flight path would be off
distance proportional
(t+32),
for pilot error was
outside the normal
not studied.
76
However,
could
these inaccuracies
all be eliminated by
sub-
stituting for Vm the present groundspeed based on last position and time between position updates.
speed is
unlikely to vary quickly
interest
(32 seconds),
it
Because ground-
over the time
is more easily applied in vertical
navigation than in time control where the time
interest
is generally far
interval of
interval of
larger.
TIME-CONTROLLED NAVIGATION
4.2
Several design objectives for
follow naturally
the time-controller
from the discussion in Chapter I:
1. The system should be closed-loop so that in
the presence of wind, inaccurate equations, or
pilot error it issues continuous corrections to
A feedback system will
the required airspeed.
compensate for inaccuracies in the equations
by not permitting errors to propagate.
2. The system should optimize the flexibility of
the aircraft to arrive earlier or later than
the assigned time by equal amounts.
The latter objective implies
cally
that the system will periodi-
possible time of arrival
compute the earliest
Using these,
latest possible time of arrival.
the
time differences T I and
T
= ATA
-
12 = LPTA
This is
shown
T 2 in
-
let us define
the following manner:
EPTA
(4-3)
ATA
(4-4)
schematically for
the waypoint in Figure 4-2.
and the
some arbitrary distance
from
77
TU
T22
1
I
0
EPTA
~
Fig. 4-2
Using these
jT
1
-T 2 I by
to change airspeed to one
speed,
will
not
airspeed.
should
be
aircraft
extreme, minimum or maximum air-
change until
T 1
=
T2
time bound,
(i.e.
maintain the same value of T1).
if
T
2 >
LPTA or
U1 , we
to decrease T 2 and to
fast as possible in order
fly as
It
initially requires the
that the corresponding
in order
EPTA, does
system is required to minimize
an appropriate
that this objective
obvious
LPTA
Time Differences
terms, the
choosing
t
ATA
This process was
shown in
Figure 1-4.
A controller
but,
based on these objectives
is sometimes the
as
quantity, it
was
constructed,
case when striving
to optimize a
type of
control which
produced a "bang-bang"
commanded either minimum or maximum airspeed for any
tion other
than equality of TU
relative size of
nored;
and 1c2*
the difference between
the controller
In other words,
T
and
r2 was
the
ig-
responded identically to a difference
in the'time flexibilities of one minute or one
repetitive acceleration or deceleration was
table as
condi-
a method of controlling the
second.
This
totally unaccep-
aircraft.
Therefore, a
78
third objective was
added:
3. The airspeed changes commanded to optimize
flexibility should be sensitive to the magnitude of the error.
A controller
described
designed to meet
these
three objectives
is
in Section 4.2.4 following the discussion of the
feedback nature of
the system and the method
of computation
of EPTA and LPTA.
The time
FEEDBACK CONTROL
4.2.1
in Figure
4-3.
control
system is
shown
The feedback loop has been broken into parts
labeled A and B to designate the separate functions performed
at
each stage.
In block A
using distance to
position),
waypoint if
and
present
the EPTA and LPTA are
the waypoint
(determined from aircraft
airspeed, and the desired airspeed at the
specified.
Block B uses the ATA to
as required for determining the command
T2
using present position and airspeed to
the
system corrects for pilot
which
enter in the
tion or
computed
compute
T1
airspeed.
By
compute EPTA and LPTA
error or wind disturbances
forward loop.
Errors in measuring posi-
airspeed are in the feedback path and will affect
the
accuracy of the solution.
The two feedback loops
of Figure 4-1
vertical navigation controller and
troller, have common inputs
to
the
and 4-3,
the
time navigation con-
the feedback path of three-
dimensional position and measured true airspeed.
Increased
airspeeds commanded for time control purposes are
sensed as
79
changes in both position and measured airspeed by the vertical
These require greater command
navigation controller.
rates
of
and result in new altitude values for
tions
are accomplished three times per
ing subroutine FORD1 in Appendix B)
command indications
feet;
that
transition smoothly.
the altitude changes
speed by
4.2.2
so
second
the horizontal position changes by
second,
less
computa-
(see the callin
the changes
In one
third of a
less than 300
less than 30 feet;
and the
air-
than 1 ft/sec.
COMPUTATION OF EPTA AND LPTA
the commanded
the next cycle
Both controller
command airspeed computations.
descent
Figure 4-3
shows
that
airspeed is a function of EPTA and LPTA;
therefore errors in their determination directly influence
the
time accuracy achieved.
The ATC scheduling
algorithm
described in Chapter I performs a one-time computation
is
at a large distance
EPTA and LPTA while
the aircraft
from the waypoint.
The on-board computation, on
hand,
is
the other
performed repetitively for shorter and shorter dis-
tances as
the aircraft approaches the waypoint.
the method
Therefore,
of computation varies with the remaining distance.
This will be illustrated
the same
of
logic applies
and deceleration
for the
computation of EPTA, but
in computing LPTA with acceleration
interchanged and minimum airspeed substi-
tuted for maximum.
Figure
4-4 depicts
the velocity
profile
for
a Boeing
40
Standard day
JT3D.3B engines
- - - Nonlimiting values
Limiting values
Initial
buffet
speed
35
/
-Thrust limit
/
/
30
0
6
I
*6
25
Q/,//
00
20
15
Minimum
maneuver
sp-
10
0
200
I
250
I
300
350
I
400
I
450
Velocity (knots true airspeed}
Fig. 4-4
Velocity Profile 707-320B
1
500
550
81
707-320B.
permitted
indicate the extremes of
The heavy lines
in the present simulation.
permissible operating
(or LPTA).
EPTA
(or minimum)
temporarily the effect of a change
in altitude, the computation has
1.
data is
This
available for the computation of
altitude is
Ignoring
error.)
so that maximum
in the on-board computer
airspeed at any
inside the
range for a 225,000 pound aircraft,
allowing a buffer zone for pilot
stored
(These are
airspeed
three stages:
At large distances from the waypoint, the aircraft can accelerate to maximum airspeed for
that altitude (VMAX (h 0 )), cruise at that maximum and then deceierate to comply with airspeed
However,
restrictions at the waypoint (V(hWP)).
at some point the distances required to accelerate and decelerate leave no distance to
cruise.
2. After this point the aircraft can only accelX (h0) and
erate to some airspeed less than V
is t ance.
still decelerate in the remaining
3. Finally the aircraft reaches a point where it
can only decelerate (or accelerate if below
airspeed) in the remaining
the required final
distance to achieve the desired airspeed at
the waypoint.
The computation of EPTA is performed
MXASP
in the subroutine
in Appendix B.
In
the present study,
the acceleration and
deceleration
values used in computing EPTA and LPTA are assumed to
equal
and
invariant with altitude.
1.75 ft/sec2 and was based
makes
chosen was
on some experimental measurements
done with the aircraft model
[2]
The value
be
of Chapter II.
the same assumptions
The Boeing study
and chooses a value of
.125 g
82
(4 ft/sec 2)
which was
not achievable
Victor measured
Capt.
[3],
In his studies
described here.
in the aircraft model
deceleration values for the actual Boeing 707-323 aircraft
and
simulator at various alti-
the American Airlines 707-323
The
tudes.
deceleration decreased with altitude and varies
with airspeed but he obtained
feet of
1.4 knots/sec
an average value at
10,000
(2.37 ft/sec2 ).
The acceleration and deceleration values chosen could
be made unequal without any additional programming of
simulation.
They could be made a function of altitude
anything other
than constant for one
computation intractable.
solution is that
corrected for by
tion and
It is
only when very close
to
acceleration and deceleration
accuracy.
For
the
feedback
or acceleration other
sensed as an
changing
they were
altitude would make the
The beauty of
actual deceleration
than the assumed value will be
that
To assume
with some increased complexity.
present
the
the
error
in posi-
commanded airspeed.
the waypoint
that
the
rates may affect
example, in stage 3 of the
the assumed
time
computation de-
scribed above, an actual deceleration greater than the 1.75
ft/sec2 value used
in predicting EPTA would put
the
aircraft
into stage 2 and the commanded airspeed would adjust accordingly.
stage
An actual deceleration
3 would not meet the
waypoint, but this
less
than 1.75
ft/sec2 in
time or airspeed desired at
the
is a conservative value and could be
attained by deploying
the spoilers.
Actual acceleration at
83
maximum
thrust which
is below the
more difficult problem.
being below 250 knots
generally
suffer
There is no
penalty associated with
the time accuracy would
but
if the chosen value of acceleration
appear to
here, but
could
not be achieved
be a factor in any
the assumption that
be achieved at high altitude
tests conducted
led to
errors in computing EPTA
AVERAGE AIRSPEED DURING DESCENT
1.)
the waypoint
If
includes a descent
(or LPTA) is adjusted for
the remaining
the
computation
the variation in maximum
(or minimum) airspeed with altitude.
As shown in Figure
can fly at its greatest true airspeed
at approximately 25,000 feet.
mance window of
spread
(This
ft/sec2 acceleration could
4.2.3
the aircraft
in practice.
1.75
stage
of EPTA
for stage 3 used
of the
during
distance to
is a
(the waypoint airspeed restriction
considered here),
in the calculations
did not
assumed 1.75 ft/sec2
To
exploit
4-4
(VMAX( 2 5K))
the full perfor-
the aircraft and gain the maximum delay
the computation must include the variation of maxi-
mum airspeed at each altitude.
Because the descent
profile of Figure 1-1,
is confined to
the linear descent
the rate of descent
required to main-
tain the profile is greater for higher true airspeeds.
the aircraft
speed and
spends less
time at
this factor must be
altitudes of high
included when
average true airspeed during the descent.
Thus
true air-
computing the
The average true
84
to
airspeed for a descent from current
be determined
by summing the
increments of altitude
final
altitude can
small
times required to traverse
(Ah) during the descent and dividing
into the horizontal distance travelled:
the result
(4-5)
horiz slope distance
n
Ah-coty
V
AVE
VMAX (h i)
n = number of altitude increments.
where
In
the present
descent was
simulation, this variation in rate of
ignored in favor of a computationally simple
approximation.
As it
is presently computed in the subroutine
MXAVR of Appendix B, average airspeed
is determined by the
following weighted average:
VVAVE
=V
=L2+
VMAX(h 0 )+V max( 2 5 K)
a
2
MA
(h 0-25,000)
(hh
VMAX(25K)+VMAX(hWP)
MAX
2
MA
+
WP
, 000-hg
P-(25
(0-hWP)
(4-6)
for h 0 > 25,000 ft.
And,
V AVE
VMAX (h0 )+VMAX (hWP)
2
for
Although this was originally felt
h 0< 25,000
ft.
to be the source of
(4-7)
some
85
error
in the
computation of
value of VAVE
EPTA prior to
computed for 1,000 feet
the
descent,
the
altitude increments
in
Equation 4-5 differs from this approximation by a maximum of
for h0
1.4%
35,000 ft and h P =
=
10,000 ft.
The relationship
COMPUTATION OF COMMANDED AIRSPEED
4.2.4
governing commanded airspeed
(VC) was
of the design objectives and
is
chosen by
inspection
expressed by the following
equation:
2
C
=
1
MIN
Ty
T1
In
and
this
+
T2
+T1
2
expression T 1 and
4-4 and
mined
2
'
'
(4-8)
MAX
22
T2
are defined by
the airspeed extremes VMAX
equations
and VMIN
are
4-3
deter-
as follows:
1. During stage 1 of the computation of EPTA and
LPTA as described above, the airspeed extremes
I' are the aircraft's maximum and
V
' and V
11AZ
. MIN
minimum airspeeds for the current altitude
(VMAX(h0) and VMIN(h0)) as shown in Figure 4-4.
2. During stage 2 of that computation, the airspeed extremes are the maximum or minimum airspeed which can be achieved in the remaining
distance and still decelerate or accelerate
to the desired airspeed at the waypoint.
3. During stage
set equal to
the aircraft
achieve that
Thus the values of
MNASP
V MAX'
3, the airspeed extremes are both
the desired final airspeed so that
will decelerate or accelerate to
airspeed.
and V MIN'
subroutines of Appendix B and
are
set in the MXASP
and
the commanded airspeed
86
is computed in the CMSPC
The relationship of
subroutine.
equation 4-8 was
all the design objectives.
The true airspeeds commanded
(converted to Mach above 25,000 feet and
below 25,000) are very stable and
change
required is
minimum airspeed when the quantity
in the next
4.2.5
the
indicated airspeed
only large airspeed
the initial change to
experimental results using
expected to meet
|T 1 -T
near maximum or
2
is
large.
this approach will be presented
chapter.
EFFECT OF WIND DISTURBANCES
This
control scheme was
tested under zero wind conditions and subsequent
might
reveal that
some modifications
effects are included.
algorithm
4-4
[2]
For
studies
are required when wind
example, the Boeing scheduling
converts the true airspeed profile of Figure
to a groundspeed
This is
profile by applying forecast winds.
necessary because
any along-track winds
or tailwinds) will alter the achievable
(headwinds
EPTA and LPTA.
the
controller design contemplated here will attempt
the
time differences T 1 and T 2 equal
available estimate of EPTA and LPTA.
by this approach and the closed
suggest
well for
The
that it might
to hold
based on its best
The
flexibility
loop nature of
have the capacity to
any along-track wind disturbances
the EPTA or LPTA.
But
the
implied
solution
correct very
that would alter
87
CHAPTER V
EXPERIMENTAL RESULTS
as
puter,
the
computer and
the
to
used
radar
tal
position.
immediate
an
commanded
pilot's
would align
lots
as
the airspeed needle
it was
This was
easily
instruments
the
flight
The
testing which has
the
algorithm which
in
this
to
chapter.
judged quite
(known as
been done
positions
into
the
on
these
the
to
airspeed
Chapter
and
IV).
inputs which
descent needle with
acceptable
their
by the
normal scan
instrument
the
added
in
control
or vertical
1-5)
horizon-
were
described
making
incorporated
but
Figure
(cf.
commanded
as
hC
and
reduced
task was
command bug.
the
(VC
rate
descent
display
to
indicator
velocity
vertical
devel-
the weather
aircraft's
"bugs"
study,
present
the
For
the
to
reference
occupies
copilot
and
information
Situation Display
Traffic
the pilot
the
by
(which was
display
information)
traffic
position between
provides
moving map
an Airborne
here without
and
The
the
Also,
tested as
and
oped
is
pilot.
drawn
are
the
in
described
present new
to
at will
changed
may be
instruments
flight
The
chapter.
previous
scheme
on-board navigation
ideal
is
Appendix A,
in
and
com-
digital
the Adage
interfaced with
Chapter I
described in
testing
for
mockup
cockpit
The
aircraft
command bugs
piof
crosscheck).
model
are
and
of
summarized
88
AIRCRAFT MODEL EVALUATION
5.1
designed
closely
to
approximate
Boeing
707-320B.
evaluations
consisted
of
a
the
performance
of
the real
tests was
to
compare
these
and
coefficients
(C
tively) were
chosen -
1
and
6A
C
m
of
acceleration,
descent,
pitch
the
of
that
to
real
response
2-20
and
aircraft.
control col-
to
because
Equations
of
primary purpose
The
considered possible
were not
inputs
umn
roll
the
of
tests
Unbiased
simulation
the
deceleration of
familiar with
by pilots
aircraft.
climb,
first performance
the
of
one
tests
flight
of
characteristics
aerodynamic
the
Therefore,
aircraft model was
the
Chapter II,
described in
As
these control
and 2-21
respec-
d
for
accurate
lack of
data -
by
trying
*
is
There
of
formance
less
than
consensus
in
the
Carl W.
until
values
various
of
aircraft model but
satisfactory by
was
response was
quantitative way
no
the
the desired
that
parameters
it
anyone
adequately
required
for
in
measuring
no
engaged
in
present
the
the
total per-
the
case was
simulated
the
obtained.
it
rated
testing.
real
study.
The
aircraft
Captain
Vietor of American Airlines, who has 26,000 hours of
It must be pointed out here that, while the aircraft model was
designed to be accurate over all altitudes, airspeeds, and configurations normally flown by the 707, the final value chosen
for C1 6 A was judged by the pilots in these tests to be insufIn the actual aircraft,
ficient in the landing configuration.
additional aileron surfaces (the outboard ailerons) become opThese may need to be
erative when the flaps are extended.
modeled by anyone employing this simulation in the landing phase.
89
time and 6,000 hours
flying
of that
in the Boeing
707-320B
this comment:
offered
"The aircraft is accurate in its inertial
functions, power functions, and control
functions so that it is an acceptable base
In short,
for extracting the data needed.
the simulation is quite realistic."
available for the time required to
tor in
Airlines
707-323 simulator by Capt.
ments [3]
225,000 pounds.
effect
have shown
5-1.
Note
for
longer at
simulation
Vietor's experi-
differences have only a small
For example, in one
247,000
of
that the weight
a deceleration from 365 knots to
only 5 seconds
The basis
supplied by him.
Vietor and
However, Capt.
that weight
on deceleration time.
10,000 feet,
fac-
simulator varies while the MIT
the American Airlines
fixed at
concept.
a crucial
tests made in the American
data from flight
The results are shown in Table
is
decelerate -
the time-controlled navigation
comparison is
evaluation is
A quantitative
DECELERATION PERFORMANCE
5.1.1
pounds
test at
took
200 knots
than at
190,000 pounds
[3].
The
14%
results shown in Table
at 10,000
feet
tion segment).
altitudes,
as much as
(an important altitude due to
The results are
but are consistently
for comparison.
5-1 are in error by as
generally better
greater than
A mitigating factor is
10 seconds
that
much as
the deceleraat higher
the times used
times may differ
from test to test because of pilot
error
90
TABLE 5-1
DECELERATION CAPABILITY RESULTS
WEIGHT*
(lbs)
TRUE AIRSPEED
(KNOTS)
ALTITUDE
35000
25000
20000
15000
10000
5000
*
247,000
247,000
250,000
228,000
210,000
194,000
TIME (SECS.)
MIT
AMER. AIRL.
SIMULATOR
SIMULATOR
ERROR
509
447
402
358
0
60
120
157
0
54
120
168
7%
513
435
371
326
297
0
60
120
165
198
0
61
123
178
213
8%
520
407
343
302
275
0
82
142
184
214
0
78
148
198
230
7%
462
376
313
280
250
0
66
125
158
180
0
68
133
165
205
14%
433
348
258
240
0
55
135
155
0
62
159
176
14%
270
238
220
0
33
53
0
35
59
11%
MIT SIMULATOR WEIGHT 225,000
lbs IN ALL CASES
91
were
(all tests
flight
to level
in correcting
flown manually
Neverthe-
Table 5-1 is an average over several trials).
and
to
shown
the model was
less,
decelerate slower than the commer-
cially-produced simulator.
force due to idle thrust and
The difference between the
the
opposing
level
flight.
nearly
force
to drag
due
the
Because
matches
the
Equation
data
thrust
(shown
if anything, greater than the actual aircraft,
are,
error
advanced as an explanation.
.7
The
slightly high above this
at 35,000 feet
the time to decelerate to 447 knots
Whereas,
the time
The times in
(see Equation 2-17).
For example, 509 knots
fast.
and 2-7
the aircraft changes
drag on
Table 5-1 indicate that the drag is
too
Figure
in
drag can be
proved correct and only an error in the low speed
value.
so
The program logic and scaling have been
is surprising.
at a Mach number of
2-25
in Figures 2-6
and the drag approximations shown
2-11)
of
approximation
idle
available
in
the deceleration
determines
or
.78 Mach
the deceleration from
(358 knots)
is 11 seconds too
.88 Mach and
is
is
(402 knots)
.7 Mach
slow.
6 seconds
Therefore,
it
to
.62 Mach
is
supposed that the low speed drag of Figure 2-6 is not used
in
the American Airlines
drag terms which the MIT
5.1.2
CLIMB PERFORMANCE
simulator or that
simulation has
there are significant
failed to model.
The most difficult
be imposed on this simulation is probably
test
that could
to compare time
and
92
flight manual values.
distance climb performance to the
tests
but
not only the variation of maximum thrust with altitude
as well.
The climb
flight manual [15]
as
schedule used
a constant
Mach to
.78
complied with below 10,000 feet or
climb was measured
if the
schedule was flown as
Therefore, the climb
For example,
to 25,000
(11-3) for
feet.
The MIT
minute over the flight manual value.
puted in the
same manner.
The
(13-6)
minute or one
flight manual values
imprecise times.
be considered exact
com-
are obvious-
distance values were
computed by the author using the published average
these
to climb
Distance errors are
ly rounded to the nearest minute and the
speed and
sche-
simulation requires 8 min-
The error is +1
the same climb.
the climb
the
the flight manual indicates
7 minutes
the actual aircraft requires
from 11,000
doubt about
is no
value where there
dule being followed.
utes
computed
difference between each successive altitude and
11,000 feet
that
until
cruise alti-
stated and the error values shown in Table 5-2 are
from the
707
250 knot FAA restriction was
It was not clear if the
from takeoff.
in the
is stated
320 knots indicated
Mach and then a constant
reaching .78
tude.
and airspeed conver-
linearized atmospheric variables
the
sions
This
climb air-
The error obtained is not to
for these reasons but the general climb
performance shown in Table
5-2 was
considered very good.
There was no data available for
or descent performance of
comparing accelerations
the model to the
real aircraft.
But
TABLE
5-2
SIMULATOR CLIMB
ALTITUDE
(1000 f t)
AIRCRAFT*
TIME (MINS.)
SIMULATOR
TIME (MIN S.)
ERROR**
(MINS.)
PERFORMANCE
AIRCRAFT*
DISTANCE (N. Mi. )
ERROR**
SIMULATOR
(N. Mi.)
DISTANCE (N.i.)
26
20
0
32
26
0
5
0
38
30
-2
9
6
0
45
36
-3
19
10
7
0
52
41
-5
21
10
8
+1
54
49
+1
23
12
9
0
67
56
-5
25
13
11
+1
75
66
-3
27
14
12
+1
84
74
-4
29
15
13
+1
92
89
+3
31
16
15
+2
100
102
+8
33
17
17
+3
108
113
35
19
18
+2
129
123
11
6
3
13
7
4
15
8
17
*
AT 230,000 lbs
**
SEE TEXT FOR METHOD OF COMPUTATION
(FROM 707-300
SERIES
OPERATING MANUAL[15])
+11
0
94
acceleration is
thrust
a measure of the difference between maximum
aircraft drag and these
and
for small angles
performance
same
forces determine climb
Descent performance is
of climb.
four
results were considered applicable to the
tions
of interest.
expected to maintain
the same angle of
in a clean configuration
descent as the real aircraft
(gear,
spoilers retracted).
TIME-CONTROLLED NAVIGATION EVALUATION
5.2
Because accurate navigation
goal
of this
pilot and copilot to
to
For
communicate
the solution which
example, thumbwheel
the ATC assigned route-time
the simulated on-board computer.
was entered by the test evaluator and the
But
speed, or
only
to
enter any assigned
evaluated.
altitude, air-
time of arrival at one of four waypoints.
two waypoints were used and
airspeed were 10,000 feet and
assigned time of
achievable
this data
increased pilot
workload which might have been required was not
Programming was provided
the primary
throttle quadrant between the
switches were installed on the
profile
in time was
research, many aspects of
might have been tested were not.
of
flight condi-
Because of the error in deceleration, the
aircraft model was not
flaps and
so the previous
the same way,
related to deceleration in much
arrival was
and descents were
25,000 and 35,000 feet.
However,
the assigned altitude and
250 knots
varied over
in all cases.
the range of
The
times
conducted from cruise altitudes
The
routes flown are shown in
95
Figure 5-1.
The 35,000 foot
cruise along J152
(the air
route from Hampton to Providence) was initiated approximately
30 miles prior
are
the 120+
25,000
to
foot
to intercepting
initial distance values shown in Table 5-3.
cruise along V-2-14
(the air route
descent point.
the
distances
of achievable arrival
Gardner.
would
Note
aircraft
have little
This
fix was
to
should be made
the time accur-
effect on
large distance remaining
for the feedback control to
were
tested
first column of Table
and
are designated
5-3.
line captain with 26,000 hours of
2 is
along V-2-14,
correct
the
to the time schedule.
Four pilots
in the
that,
change that
achieved here because of the
after Griswoldville
the
pilots flew directly from Albany
The 11 degree heading
at Griswoldville
acies
traveled influence
intermediate fix at Griswoldville.
emphasized and most
to the
but not the accuracy of
times
time-controlled navigation.
there is an
not
The total
The
from Albany
30 miles prior
Gardner) also began approximately
range
These
the descent profile.
Pilot
the numbers
Number 1 is
flying time.
an airline pilot with 2,000 hours of
by
an air-
Pilot Number
flying time.
Pilot Number 3 is a military Senior Pilot with 5,000 hours.
The fourth pilot
is the author,
a military pilot with 2,000
hours.
Two
of
the pilots
tested, Numbers
experience performing unrecorded
1 and
4, had previous
time control tests
during
II
W
qW
W
1W
w
CRUISE ALT.
25,000 ft.
ARRIVAL FIX
10,000ft.
250 KIAS
UP.~l
ACTON
GDM
110.6
mo0o
IN
ALLDISTANCES
ARENAUTICAL
~L7IO~
ON'
MILLIS
BOIS
112.7
CRUISE ALT.
35,000 ft.
Fig. 5-1
Map of Routes Flown
ARRIVAL FIX
10, 000 ft.
250 KIAS
97
TABLE
EXPERIMENTAL
(TIMES
IN MINUTES
5-3
RESULTS
PLUS
SECONDS)
INITIAL CONDITIONS
TEST NO.
DIST(N.Mi.)
EPTA
LPTA
ATA
ARRIVAL
TIME ERROR
(SECS.)
AIRSPEED
ERROR
(KTS)
lA
125.4
17+10
26+10
22+00
26
6
1B
95.4
12+41
21+04
18+00
22
3
iC
124.8
17+12
26+11
18+30
53
6
1D
95.2
12+43
21+06
20+00
20
5
2A
86.5
12+52
20+26
15+00
26
2
2B
121.5
17+16
26+07
19+30
25
2
2C
122.8
17+16
26+12
25+00
16
3
2D
93.5
12+45
20+59
20+00
14
6
2E
92. 5
12+48
21+01
16+00
21
5
3A
94.8
12+45
21+10
17+00
20
11
3B
123.2
17+14
26+09
22+00
14
9
3C
93.2
12+47
21+10
18+00
12
6
4A
90.9
12+54
21+22
18+00
12
7
4B
93.0
12+46
20+52
15+00
17
21
4C
94.1
12+45
20+59
15+00
+
21
-
1
98
flown the aircraft
Pilot Number 2 had not
development.
simulation described in Chapter II but
were permitted one unrecorded practice test before
simulator and Number
experience in this
with only 2 hours of
commencing
Number 3
significant that
is considered
It
recorded runs.
2 and 3
Both Numbers
the cockpit mockup.
tests using
other
participated in
has
2 with no experience flying this particular aircraft
tion achieved comparable results to
bugs.
is a measure of the
This
of communicating the
rates by bugs on the
2D are
than
greater
of
T
T,
=
In all cases,
.
time-control mode was
teristics.
A
a commanded
airspeed
ferences
smaller
large
require
the
3A, and
less
T
lD,
1 being
and 4B are
examples
3B are examples
of
the commanded airspeed, when the
reflected the desired charac-
difference between
commanded
mediate value.
2A, 2B,
selected,
of
Tests number
time difference
Tests number
Tests number lA,
2 > T
T
command airspeed and descent
arrival were chosen at various
examples of the
T 2.
the simplicity of
to
in the range of achievable times.
and
2C,
actual
instruments.
The assigned times of
points
navigation command
similarity between the
aircraft and the simulation and attests
the method
who were more
the pilots
and the
familiar with the aircraft model
simula-
one
of
the
correction.
airspeed
T
and
extremes
As
adjusts
the
IT
T2
results
in
small
dif-
while
-
smoothly
T 2 1 gets
to
an
inter-
99
tests performed here were flown under no-wind condi-
The
The number of
tions.
significant
performed
tests
required to obtain statistically
data under various wind
Nevertheless,
in the time available.
are a necessary step
results
could not be
conditions
in confirming
the present
the validity of
the navigation concept.
TEST RESULTS
5.2.1
The results achieved
shown in Table 5-3
tests
during
and in numerous
in the formal
unrecorded tests
the final stages of development show
in principle
that the navigation controller assists the pilot in navigating along
four-dimensional routes.
Unfortunately,
refinement of the logic is necessary for
The
tion to work perfectly.
at
cruise altitude is
not
the present simula-
initial value of EPTA computed
actually achievable because the
as discussed
assumed rate of acceleration at high altitude,
in Chapter IV,
is unattainable.
was not included
reason.
test
the
1C,
Test number
in the accuracy calculations
Shortly after
1C in Table 5-3
for
this
descending through 25,000 feet during
the EPTA displayed on the moving map
time assigned was not
the route was
some
achievable and
flown in such a manner
indicated that
the remainder of
that the actual
time of
arrival has no significance.
Deviation from the assigned descent profile was not
measured but was judged to be within
zone allotted to pilot error.
In all
the bounds
cases,
of any buffer
the vertical
100
controller "flared"
descent
rate of descent
intercepted
in the
last
the aircraft by decreasing the
the final altitude approximately 14 miles
the waypoint.
in
However,
no
Pilot reaction to
Pilots
the final airspeed.
the control system was generally
familiar with the
2 and 3, who were not
find that
to
navigation concept described here, were upset
the initial commanded airspeed might be far different
finite acceleration and decelerations
and the pilots
changes would
initial airspeed change but
5.2.2
ACCURACY ACHIEVED
listed
in Table 5-3,
mean of +19
The
overall
excluding test
MNASP
1C,
It
is
tests
described by a
(la)
is believed that the bias
of the logic
Many of
the subroutines
ing this research were tested off-line by
puts.
the
error for
about
the
could be
for computing
(These are computed in subroutines MXASP and
of Appendix B.)
assembly
speed.
considered necessary.
this was not
eliminated with further refinement
LPTA.
the bug
smoothly command the
seconds and a standard deviation
mean of 5 seconds.
EPTA and
to
compu-
smooth airspeed
soon discovered that
could be modified
in the
are used
catch and subsequently maintain
The program logic
from
However, only
the cruise airspeed they were maintaining.
tations
from
14 miles
entire
case were the
required to decelerate or accelerate to
favorable.
the aircraft
Thus
1,000 feet.
developed dur-
iterating
the
language logic through a wide range of possible in-
This should also have been done for the
subroutines
101
which compute EPTA and LPTA, but
in
plished
the time available.
EPTA and LPTA presented to
check was not
this
accom-
The alphanumeric
readout of
three
discontin-
the pilot
shows
uous jumps at distances from the waypoint which are known
decision points in the
discontinuous jump in the
flexibility.
optimize
This,
logic.
of course,
commanded airspeed as
Refining the
discontinuities might eliminate
causes a
to
tries
it
logic to eliminate these
result in a
the bias and
more accurate determination of EPTA and LPTA at cruise altitude as well.
The merit
of closed-loop continuous corrections was
particularly noticeable during
to the waypoint.
The pilot's diligence in flying
manded airspeed during the final minutes
largely determined
5.2.3
of approach
last stages
the
the arrival
FAILURE TO OPTIMIZE
of
the
accuracy in seconds.
FLEXIBILITY
The
time navigation
bility.
From early November when Equation 4-8 was
derived,
through the testing,
this report,
been met.
flexifinally
and through the writing of the
it was assumed
that
this
objective had
The EPTA and LPTA displayed in the cockpit both
changed with time but
the airspeeds commanded appeared to
equalize the flexibility.
the
com-
approach
controller was designed to optimize the aircraft's
bulk of
the
It was
considered unlikely that
idealistic form of the delay spread shown in Figure
(with EPTA remaining constant) would be
1-4
achieved in practice.
102
The flexibility of
times
the approach was demonstrated numerous
The commanded airspeed would
descent.
and
the EPTA and LPTA would begin to
was
thought)
to obtain an analog plot of the
most
of
The result for
It is now obvious
that
been made
time history of EPTA and LPTA
Finally,
after
completed, a digital program was
the testing was
test.
(optimally, it
converge
was not accomplished.
written to save EPTA and
the
the
immediately change
Several attempts had
to the new ATA.
during a test but this
during
time of arrival
changing the assigned
by
LPTA at 30 second
test 4C
is shown
intervals during
in Figure 5-2.
the controller will navigate
quite
consistently to any achievable assigned time of arrival
(plus a 19 second bias),
bility
but is
is not
optimizing the flexi-
in the manner desired.
One possible explanation for
the bang-bang
this failure
system
type of control
could be that
described in Chapter IV
with its undesirable qualities was actually the optimal
solution.
The commanded airspeeds of Equation 4-8
stable and easier to
defined here.
and
sacrifice flexibility
However, a complete analysis of
the source of
5-2, must
fly but
the bias,
so
await further study.
are more
as it
is
this failure
clearly demonstrated
in Figure
103
0
TIME
TEST 4C
0
-20+00
-19+00
0
eL
-18+00
P
4
Goo
0-16+00
.
..
.
.--.
.
-.
0**
0
'--.
100
25
50
75
DISTANCE TO WAYPOINT (MILES)
Fig. 5-2
Delay Spread Time History
*
- ATA
-14+00
0
Goo
$
13+00
12+00
104
CHAPTER VI
ACCOMPLISHMENTS, RECOMMENDATIONS, AND CONCLUSION
the course of this research, the following
In
objectives
have been achieved:
1. The creation of an aircraft model which closely
approximates the available aerodynamic design
data for the Boeing 707-320B for altitudes from
sea level to above 35,000 feet and airspeeds
within the 707's operating range (excluding
takeoff).
2.
The creation of an atmosphere model in which
density and the speed of sound (a function of
temperature) vary in accordance with the ICAO
standard atmosphere.
3.
The development of analytic relationships and
display programs which permit cockpit indications of indicated airspeed and Mach.
4.
The design of a feedback control system which
assists the pilot in maintaining a fixed,
linear descent profile in space.
design of a feedback controller which
5. The
assists the pilot in meeting assigned times of
arrival at three dimensional waypoints subject
also to a speed constraint at the destination.
An additional objective, that
the airspeeds commanded would
delayed
optimize the amount the aircraft can be advanced or
around
the assigned time of arrival, was
not achieved.
The aircraft model and navigation controller were simulated
base
on an Adage AGT-30 computer
707
cockpit mockup.
interfaced with a
The simulation was coded
efficient assembly language programs which:
fixed-
in highly-
105
1.
Solve the aircraft equations of motion 15 times
per second using sampled pilot control inputs.
2.
Solve the navigation equations 3 times per
second and display a command airspeed bug and
a command descent bug on the corresponding
In addition, an alphacockpit instruments.
numeric readout of the earliest possible time
of arrival and the latest possible time of
arrival are presented to the pilot.
3. Update the flight instrument readings (7.5
times/sec), translate and rotate a moving map
(15 times/sec), and draw all cockpit displays
(The flight instruat 30 frames per second.
ment and map programs were modified and adapted
for this study, but are not the original work
of the author.)
The aircraft simulation was
sional
pilots
troller.
to
flown manually by profes-
test the accuracy of the
Simulated approaches from cruise altitude to
initial approach fixes
for Logan International Airport were
flown under no-wind conditions.
The
aircraft was
be a very realistic model of the Boeing
found
the
initial approach fix.
times
In a total of
accuracy was achieved
the controller
in meeting
(or bias)
2. A standard deviation
of 5 seconds.
explained in Chapter V,
14
tests
the
specified arrival
of 19 seconds.
(la) about
the mean error
the bias value can be reduced or
eliminated by further refinement of the program logic.
variation about
fol-
see Chapter V):
(for complete results
1. A mean error
As
707 and
to
judged
to be helpful in complying with assigned times at
was
lowing
navigation con-
the mean was
The
considered to be well within
106
the accuracy requirements
of an air
assigned times
value is
primarily a measure of
influence of pilot
system
control
However,
of arrival.
based on
under the
traffic
the
five second
the navigation controller
errors in position
If
error.
and airspeed are introduced and wind errors are
included,
number will increase.
this
During the development
of the
controller,
the following
on the
simplifying assumption was made which bears directly
results:
1. The acceleration and deceleration capabilities
of the aircraft were assumed to be constant,
equal, and invariant with altitude.
The assumption of constant acceleration and deceleration
between
any two
airspeeds was felt
effect on the accuracy of
the value of deceleration.
the
flight is
(see Chapter V)
computed earliest possible time of
35,000
lower
than
because
arrival was based on
acceleration of 1.75 ft/sec2 at
feet.
could be more
Both acceleration and deceleration
ately
generally
the
the reduced thrust available.
test result
an unattainable level-flight
However,
Also, acceleration decreases with
altitude because of
led to one invalid
This
(especially consid-
the system).
value of acceleration in level
increasing
have only a minor
the controller
the feedback nature of
ering
to
specified by further study.
veloped here was
felt
The
accur-
aircraft model de-
to be sufficiently
accurate to provide
107
meaningful
time
data, but
achieved
accuracy
The time
investigation.
experimental
cursory
for accelera-
in the tests, using a constant value
to
tion and deceleration, may be due
flown at
the error-correcting
Also the last
nature of the feedback control.
all tests were
than a
constraints precluded more
14 miles of
10,000 feet where the value of
acceleration and deceleration chosen
(1.75 ft/sec 2)
was
approximately correct.
RECOMMENDATIONS
6.1
The next step in
gation
require 15 to
30 minutes
each.
It was
accuracies
design.
system and
should
this
obtained under
ibility?
the
The
the command airspeed
time flexibility,
chosen to
achieve such
in the time of arrival without equalizing
The answer may lie
If
then a major question
commande& airspedes, which are
equalize the aircraft's
accuracy
be tested.
in the presence of wind.
can be confirmed experimentally,
How do
in the
feedback nature of the
of determining
achieve similar results
arises.
in
decided that
this condition reflect the merit
Conceptually, the
the method
condi-
these
obtain statistically significant results
time available, only the no-wind case would
the
test the navi-
The particular approach routes flown for
order to
of
to
concept described here under a variety of wind
tions.
tests
this research is
the flex-
in the mathematical analysis of
optimization problem which was
not performed here.
108
Along this line of reasoning, the
for further research are
tions
1.
following recommenda-
offered:
Compare the results cited here to tests conducted in the presence of wind and in the presence of uncertainty in observation of position
and airspeed.
This
2. Perform the mathematical optimization.
might provide insight into why the flexibility
was not equalized; it might suggest alternate
designs in the presence of wind or position
errors; and it might provide a benchmark of the
best obtainable performance.
It is
felt that the present approach could be
improved
and extended in the following ways:
1.
Study and define the acceleration and deceleramodel over
tion capabilities of the aircraft
the full range of airspeeds and altitudes for
inclusion in the calculations.
2. Modify the program logic so that the 15 mile
deceleration segment can be varied or eliminated for time-controlled navigation inside the
terminal area - possibly to the runway threshold.
6.2
CONCLUSIONS
This
report
summarizes
the
design,
testing of an on-board navigation concept
employed
in the air traffic control
routes
and
waypoints,
pilot
to meet assigned
The
the
future.
three dimensional
times of arrival at
intermediate
then this "navigation controller" would
in complying with minimal assistance
concept was
tested by
and
that might be
system of
If aircraft are required to navigate along
simulation,
from the
aid the
ground.
professional pilots on
a
109
simulated Boeing
707-320B described herein.
for no-wind conditions during descents
to 10,000 feet.
aircraft's
argued that
route
Because of
the way
flexibility in computing
it will correct
of flight.
The
to be applicable
from cruise altitude
command airspeeds,
concept, adjusted
or cruise profiles,
to any phase
of
the
the controller uses
for unforecast winds along
time-control
particular descent, climb,
Tests were run
flight.
is
it
is
the
for
considered
110
APPENDIX A
THE AIRCRAFT SIMULATION PROGRAM
The aircraft
programmed specifically for
simulation was
the program, see
The basic
[16].)
structure
the
coding of
was
created for a VTOL aircraft by Gordon Kemp in 1969
Robert Anderson adapted Kemp's
of
(For an explanation
the Adage AGT-30 digital computer.
[17].
program to a Boeing-supplied,
fixed-base simulator using simplified jet transport dynamics,
sophisticated flight
Traffic
instrument displays, and
extensively in the current
ment displays are
A Mach
is
the
included and
traffic
several
not included here.
mance of a Boeing
conditions.
the
full
dynamperfor-
range of operating
This program is
included and
explained here
that it is
sufficiently
accurate to serve
under the premise
as a basis for
effort.
The aircraft
to accurately model the
707-320B over
the al-
were only modified
included here.
ics were extensively revised
Likewise,
"MMAP2", and
situation display program,
rescaled and are not
instruments were
but the basic program
phanumerics display program, "CRGD2",
and
instru-
program titled "FNST2".
the present simulation,
relatively unchanged and is
been used
The flight
simulation.
contained in the
indicator was
rescaled for
This work has
[18].
Situation Display
the Airborne
research beyond
the
scope
of the present
111
The program, "ACSM2",
of
alternates between
under the control of a
("SIM11" and "SIM2")
subroutines
line-frequency,
These sequences are shown
clock-interrupt.
and documented on
two sequences
the third page of
the computer program.
in the paragraphs
The subroutines are briefly described
which follow.
The INIT
INIT
starts
The clock
the clock.
the program variables,
specifies interrupt pivots,
control input biases,
establishes
and
subroutine initializes
then assumes
the program by periodic interrupts.
Although the instrument
display programs are not discussed here, it
note that the
command "DIALS" must
to the command
puter prior
tion routine
in the CRGD2
"INIT"
control of
be entered
since it
important
is
is
into
the
to
com-
an initializa-
program which creates
several of
the vector display lists.
The first
ASPD1
is ASPD1.
and
this
routine is
is actually the
first
called after the clock-interrupt
common
of the
call the displays proceed
program
load
This
subroutine
interrupting
display routines.
independently of
initiate a new vector
The AGT-30 computer has
in nature as
only to
opposed
described under RDISC.
list.
a set of function switches
which are used to input program commands
trative
After
the main
the foreground computations
another vector or to
FNSW
to both program sequences
that are
adminis-
to the cockpit discrete inputs
The function switch assignment
is
112
The large geographical
shown in Figure A-1.
area and alti-
tude ranges used in the simulation dictated the fast move
capability indicated on switches 6,
and
of cycles
Switch number
the unused
Function switch 5 per-
execute a programmatically set number
then "freezes"
the aircraft
is a useful feature for debugging new
until the next clock interrupt.
RDISC
One 30-bit register of the AGT-30 is
A novel
The
sequence in the FNSW
routine
cockpit discrete inputs.
This
dynamics.
subroutines.
dynamics are frozen by trapping the SIM1
mits the
15.
14 and
count representing
computation time in each sequence.
the simulation to
11,
time-control studies.
8 displays a spare instruction
mits
10,
the aircraft clock and
displays
The clock switch, number 4,
strobed time used in the
7,
shared by
the
switching arrangement per-
continuously monitored inputs to be temporarily
replaced with up to
represents
4 alternate
frequencies
The remaining
selected on the navigation radios.
three are used
to communicate
One of these
30-bit sources.
in the four dimensional
studies
the selected waypoint, assigned time of
arrival, assigned altitude,
board computer.
The RDISC
register or normally
and desired airspeed
subroutine converts
connected source
It also
for
the program.
the
aircraft dynamics.
traps
the on-
to
the
selected
to flags or variables
the SIM2
sequence to
freeze
113
0
INITIAL
CONDITIONS
FRAME
BY
FRAME
DATA
OUTPUT
00
0
START
FREEZE
CLOCK
TIME
FAST
WEST
FAST
EAST
SPARE
TIME
FAST
NORTH
FAST
UP
TIME
CLEAR
FAST
SOUTH
FAST
DOWN
Fig. A-1
Function Switch Assignment
114
VCD1 and
VCD2
cockpit inputs
analog
blowdown, flap
in the aircraft dynamic equa-
for use
deployment
Spoiler
displays.
the instrument
tions or for manipulating
sample
control dial subroutines
The variable
and
in 30 seconds),
(50 degrees
throttle normalization are computed in VCDl.
The AERO subroutine computes total velocity, indi-
AERO
cated airspeed, Mach number,
the aerodynamic angles.
and
Total velocity is determined by an approximation discussed
[17].
in Gordon Kemp's original work
The aerodynamic
angles
through 2-13.
Indi-
are computed as shown in Equations 2-10
airspeed is determined
cated
from Mach number by the
rela-
tionship of Equation 3-7.
TRNSL
The TRNSL
dynamic
forces
2-17,
2-15,
subroutine computes
and
(lift, drag,
and 2-18.
and
the physical dimensions of
The
forward
it
computes thrust
the dynamic pressure
(from the ATMOS
subroutine),
in the
terms using
true velocity,
the 707-320B.
remaining aircraft dynamics subroutines
solutions of the equations of Chapter II.
accelerations are integrated using
cases
aero-
translational
side force) of Equations
In addition,
manner of Equation 2-26 and
ambient density
the
are
straight-
In all
the trapezoidal
rule:
V
n
= V
n-1
+ At
'
(3V
n
-
V
n-1
)/2
(A-1-1)
115
integra-
The earth frame position is obtained by rectangular
tion of
the vehicle frame velocities:
X
=
tion of variables and their
is performed using "B"
of an imaginary binary point
first bit, or sign bit,
also be
For
example,
shown in the comments
being
10 or
B number may
two used as
a normaliza-
the aircraft velocity, VT,
to be a B10 number.
is
implies that
This
located to
A
"B"
the right of
number followed by an "R"
the number is represented by the right
15 would be a BOR number if
means
15 bits of
word, hence a number with its binary point to
bit
position
(=1024 ft/sec) was used as a normaliza-
that 2
tion constant.
The
zero.
the imaginary binary point would be
bit
the
in a 30-bit computer word with
thought of as the power of
tion constant.
numbers where
represents
the number associated with the "B"
the
the com-
as a signed binary number between zero
The scaling
and one.
defini-
through the
scaling is available
Scaling is necessary because
comments.
puter stores values
the
thoroughly documented so that
The program is
associated
(A-1-2)
+ At Vn
Xn
its most
the
that
the 30-bit
right of
significant bits
were only in the right half word.
The control input
using
coefficients are difficult
the documented program alone.
to
decode
Rather than convert
sampled pilot inputs to the associated
control deflections
116
in degrees,
the maximum anticipated sample voltages were
related
to the maximum control deflection times
control
coefficient.
ality
The resulting
constant of proportion-
is the value used in the program.
deflections
for the 707-320B were shown
anticipated maximum voltages
the associated
The maximum control
in Table
(as normalized by
2-3
TABLE A-1
ANTICIPATED MAXIMUM CONTROL VALUES
Absolute Value
.3197
FLAPS
.3984
ELEVATOR
.4820
AILERON
.2290
RUDDER
.4490
the
the computer)
are shown in Table A-1.
SPOILER
and
117
EXPUNGE;OCTAL
TITLE ACSM2
[THIS PROGRAM CONTAINS THE BASIC INITIALIZATION OF FLIGHT VARIABLES.[ AND THE SIMULATION OF THE AIRCRAFT DYNAMICS,
[ AND THE REQUIRED NAVIGATIONAL ROUTINES.
[SUFFICIENT EXTERNAL VARIABLES ARE HOPEFULLY SPECIFIED THAT
[
IT CAN BE USED AS A WORKING BASE FOR ANY FORM OF INSTRUMENTATION
[ AND FLIGHT REQUIREMENTS,
[THE BASIC STRUCTURE IS FROM GORDON KEMP'S VTOL SIMULATION OF 6/69
6/70
C AND WAS ORIG, ADAPTED FOR MORE GENERAL USE BY BOB ANDERSON
[
REVISED 7/74 TO ACCURATELY MODEL THE BOEING 707-3208 WITH
[ P&W JT3D EINGINES AT ALL ALTITUDES AND MACH NOS BY CHUCK CORLEY
NOCARRET
ENTRY DIRCSCLCK,RETRN.MTIM1,MTIM2.KIAS..
TTIME..CLIFT.QS.,VT..VDOTGSPDALPHASIM1.
INIT.,VCD1 OVERF.,SOUND.,SSIXOM2IASO.SPDSN.
PFQRVX VYV2,UBRSLDRCLD.ESLDYSLD YCLD.RB16..
SICOSEULER..DIRCSSIMID[THRO.CARRET
-([ELEVATOR TRIM DEFINED
TRINC=25
IXZIZ=27346
[INERTIA CROSS PRODUCTS
IXZIX=30736. IXZIY=23505;
[INERTIA QUOTIENTS
IZMIY=3:3310
IXMIZ=43513; IYMIX=20203
[AIRCRAFT INERTIAS
IZZ=36763
IYY=22400.
IXX=35111;
[1/2 WING AREA B11R
SAREA"27410
[1/2 AREA TIMES SPAN B18R
SSPAN=32615
[1/2 AREA TIMES CHORD B16R
SCORD=20531
[1/4 AREA * SPAN SQRD B24R
SSPN2=36372
[1/4 AREA * CHORD SORD B19R
SCRD2=27512
MASS=3:3230
CLFLA=16:300
CLELE=22204
CDFLP=3473
CDSPL=2401
CYBET=42517
CYRUD=17070
CBETA=51776
CRUDD=14446
CPRT=47534
CMELE=64417
CMFLP =63746
CMQRT=54231
CNRRT=54631
CNRUD=56536
CNBET=35341
DFLP6=1417
DFL14=3443
DT15=21042
RHO0=23360
[MASS OF AIRCRAFT
[INCREMENTAL C SUB L W/ FLAPS B2R
DUE TO ELEVATOR B-1R
[LIFT COEF,
[DELTA CDMIN DUE FLAPS B1R
DUE SPOILERS BIR
BOR
[SIDE FORCE DUE TO RUDDER B-1R
SIDE SLIP B-2R
[ROLL COEF. W../
[ ROLL COEF. DUE TO RUDDER B- 5R
[ROLL COEF. DUE TO ROLL RATE B-IR
DUE ELEVATOR BOR
[PITCH COEF.
DUE FLAPS BO) R
[PITCH COEF.
[DUE PITCH RATE AND ALPHA DOT B5R
[YAW COEF, DUE TO YAW RATE B-2R
[YAW C:OEF, DUE TO RUDDER B- 3R
C'AW COEF, DUE TO SIDE SLIP B-3R
[6 DEGREES OF FLAPS BO
[14 DEGREES OF FLAPS B0
[DELTA T /2 15X'S PER SEC B-4R
[SEA LEVEL DENSITY E:-8R
[DRAG
COEF.
[SIDE SLIP ANGLE COEF,
118
EXPUNGE;OCTAL
TITLE ACSM2
[THIS PROGRAM CONTAINS THE BASIC INITIALIZATION OF FLIGHT VARIABLES.[ AND THE SIMULATION OF THE AIRCRAFT DYNAMICS,
[ AND THE REQUIRED NAVIGATIONAL ROUTINES.
[SUFFICIENT EXTERNAL VARIABLES ARE HOPEFULLY SPECIFIED THAT
[
IT CAN BE USED AS A WORKING BASE FOR ANY FORM OF INSTRUMENTATION
C AND FLIGHT REQUIREMENTS.
[THE BASIC STRUCTURE IS FROM GORDON KEMP'S VTOL SIMULATION OF 6/69
[
AND WAS ORIG, ADAPTED FOR MORE GENERAL USE BY BOB ANDERSON
6/70
E REVISED 7/74 TO ACCURATELY MODEL THE BOEING 707-320B WITH
E P&W JT3D EINGINES AT ALL ALTITUDES AND MACH NO.S BY CHUCK CORLEY
NOCARRET
ENTRY DIRCSCLCK,RETRN..MTIM1.MTIM2..KIAS,
TTIMECLIFTQSVTVDOTGSPD.ALPHAS1.M1,
INITVCD1,OVERF.,SOUND, SSIXOM2IAS..SPDSN,
P.,QRVXVY.VZUBRSLDRCLDESLDYSLDYCLDRB16,
SICOS,EULERDIRCSSIM1 .,DTHRO CARRET
TRINC=25
[ELEVATOR TRIM DEFINED
IXZIX=30736; IXZIY=23505;
IXZIZ=27346
[INERTIA CROSS PRODUCTS
[INERTIA QUOTIENTS
IZMIY=33310
IXMIZ=43513J IYMIX=20203;
IXX=35111.
IY'22400.
IZ=36763
[AIRCRAFT INERTIAS
SAREA-27410
[1/2 WING AREA BlIR
SSPAN=32615
[1/2 AREA TIMES SPAN B18R
[1/2 AREA TIMES CHORD B16R
SCORD=20531
[1/4 AREA * SPAN SQRD B24R
SSPN2=36372
[1/4 AREA * CHOR[D SQRD B19R
SCRD2=27512
[MASS OF AIRCRAFT
MASS=33230
[INCREMENTAL C: SUB L W/FLAPS B2R
CLFLA=16300
[LIFT COEF. DUE TO ELEVATOR B-1R
CLELE=22204
[DELTA CDMIN DUE FLAPS BIR
CDFLP=3473
[DRAG COEF, DUE SPOILERS BIR
CDSPL=2401
[SI 'DE SLIP ANGLE COEF. BOR
CYBET=42517
[SIDE FORCE DUE TO RUDDER B-1R
CYRUD=17070
[ROLL COEF. L/S[:'IDE SLIP B-2R
CBETA=51776
[ROLL COEF, DUE TO RUDDER B-5R
CRUDD=14446
[ROLL COEF, DUE TO ROLL RATE B-IR
CPRT=47534
[PITCH COEF. DUE ELEVATOR BOR
CMELE=64417
[PITC:H COEF. DUE FLAPS BOR
CMFLP=63746
[DUE PITCH RATE AND ALPHA DOT B5R
CMQRT=54231
[YAW COEF, DUE TO YAW RATE B-2R
CNRRT=54631
[YAW C7OEF. DUE TO RUDDER B--3R
CNRUD=56536
[YAW COEF. DUE TO SIDE SLIP B-3R
CNBET=35341
[6 DEGREES OF FLAPS BO
DFLP6=1417
[14 DEGREES OF FLAPS B0
DFL14=3443
[DELTA T /2 15X'S PER SEC: 7-4R
DT15=21042
[SEA LEVEL DENSITY B-8R
RHO0=23060
119
MD10 'H'F
ARXO'F
ARMD
ARMD
ARMD
ARMD
ARMD
ARMD
AR4D
ARMD
ARMD
ARMD
ARMD
ARMD
ARMD
ARMD
MD07'L;
ARMD'O
MDAR'L;
ARMD
ARMD
MD07'Lj
NOOP o
ARXO'F
S5AS*F
MD07 'L:
ARMD
NOOP
ARX0I 'F
S5AS'F
MD07'LJ
ARMD
NOOP
ARXO'F
SSAS'F
ARMD'N
MDAR
ARMD
JPSR
MDAR'L
JPSR
ARMD
MDAR'F
ARMD
MD10 'H'F
NOCP
0
RRLD
ERLD
YRLD
RRNW
ERN4W
YRNW
RSLD
ESLD
WVEL
WVX
WVY
READY
CLK1
CLK2
0
FLIPS
17777! H
RCLD
ECLD
I! H10
NOOP
CENTER HERE TO START AIRCRAFT
[MAKE SURE CLOCK IS OFF
[2ERO
FOLLOWING VARIABLES
[TURN OFF MPX 0
[SET FLIPS = -O
[COS PHI = 1 Bl
[COS THETA =1
[SAMPLE RUDDER
1 ! H4
RUDB
[ SAMPLE A ILERON
[SET CURRENT RUDDER
1! H2
ABIAS
[SAMPLE ELEVATOR
[SET CURRENT AIL ERON BIAS
EBIAS
SCALE
$SS C
[SET CURRENT
$INIFI
[INITIAL.I2E FLIGHT INST.
[RETURN TO MONITOR IN THE
[ EVENT OF OVERFLOW BUT SAVE::
[LOCATION AND VALUES
OVER F
77771
CLCK
77755
1000
CST ART CLOC
BIAS
ELEVATOR BIAS
120
CLCK
ARMD
MDAR'X
MDAS'N'F
JPAN
ARMD
MDAR
ARMD'N
JPAN' I
JUMP' I
BACK:
CLKI:
HOLD:
FLIPS:
MDAR
JUMP' I
0
0
-0
HOLD1
CLK1
4
BACK
CLK 1
FLIPS
FLIPS
,2
,2
SIMi 1
SIM2 1
HOLD I
CLCK
[COUNT SPARE
CONTI:
MDAR
MDBR
BRAE'F'N
ANBR
BRMD
NGOP
ARXO'F
ARMD
ARAR'X
JUMP
MTIM1
TIME1
MDAR
MDBR
BRAE'N'F
ANBR
BRMD
NOOP
ARXO'F
ARMD
ARAR'X
JUMP
MTIM2
TIME2
INSTRUCTIONS
[SAVE LEAST OF LAST COUNT
[OR MINIMUM COUNT
MTIMl
MTIM1
TIME1
TIME1
.- 1
[ZERO COUNTER
[NOW ADD ONE AND JUMP
[BACK UNTIL CLOCK INTER,
[SPARE COUNT IN SIM2
CONT2:
MTIM1:
MTIM2:
TIME 1:
TIME2:
[STORE AR
[INCREMENT CLK1
[SUBTRACT 4
[IF NOT 4TH INTERRUPT
[RETURN ELSE ZERO
[FLAG TO ALTERNATE
[EETWEEN SEQUENCES
[WHEN FLIPS =
[DO SIMi
[ELSE
EDO SIM2
[RESTORE AR
[GO TO INTERRUPTED S/R
9999,
9999,
9998,
9998,
MTIM2
MTIM2
TIME2
TIME2
, -1
[LARGE INITIAL
[SLIGHTLY SMALLER
121
FNSW:
ST ATS:
JUMP ,
MDIC'O'L;
S5MD
MDAR
ARBR 'K 'F
JPAN
ARAR'B'F
.JPAN
ARAR'B'F
JPAN
ARAR'B'F
JPAN
ARAR'B'F
JPAN
BRAR' B'F
JPAN
BRAR'K'F
JPAN
MDAR' A'F
JPLS
MDAR
MDAR'H'A' F
ARAR' H 'F
JPLS
MDAR
JPAN
MDAR'X
JPLS
'F
ARMD'N
ARMD
MDAR
JPAN'I
NOOP
NOOP
40 !H
FNSWS
FNSWS
IC
START
FREEZ
TIMED
FBF
SPARE
RETRN
TMCLR
F NS 10S
1463
RETRN'
KILL:
[CHECK FOR FAST MOVE
[FNSW 6,7.. 10, 11. 14,15
F MO'V E
FBFFL
, 6
FRCNT
, 4
FBFFL
RE AD
READY
FNS W
JUNMP
FREEZI
[READ FUNCTION SWITCHES
[READ FNS 1-15
[STORE FUNCTION SWITCH STATUS
[EXAMINE STATUS
[S5(6) FIRST IN BR
[SET INITIAL CONDITIONS
[S5(1) FIRST IN AR
[START DYNAMICS FNSW 2
[35(2) FIRST IN AR
[FREEZE DYNAMICS FNS41 3
[55(3) FIRST IN AR
[DISPLAY CLOCK FNSW 4
[S5(4::) FIRST IN AR
[E::<ECUTE FRAME BY FRAME
[55(7) FIRST IN AR
[SPARE TIME DISPLAY FNSW 8
[35(1 2) FIRST IN AR
[RETURN TO CALLING PGRM FNSW 13
[S5(11) IN AR(29'
[KILL TIME DISPLAYS FNSW 12
AR:,'0'F
ARMD
SUJUM
P
PE AD'(
ST A~T.'-
MD1O 'H'F
MDAP'F
ARMD
ARMD
JUMP 'I
KILL
77755
7757
I NIT
[+0 -IF
BY F, MODE
[ADD UNTIL... +0
[THEN FREEZE
[EXECUTE REST OF SIMI
[IF DISPLAY IS NOT FROZEN
[ELSE PREVENT DYNAMIC: UPDATE
[AT THIS POINT IN SIMI AND
[AT END OF RDISC IN SIM2
[SET FREEZ MODE
[FREEZE IS READY
[RETURN
JUMP' II
F.
TO THE
=
+0
MONITOR
[CHANGE CLOCK PIVOT
CCHANGE EOL P I VOT
CRETLRF.N TO CALLING PGRM
122
FNSW:
STATS:
JUMP ,
MD IiC'O'L'
S5MD
MDAR
ARBR'K'F
JPAN
ARAR'B'F
JPAN
ARAR'B'F
JPAN
ARAR'B'F
JPAN
ARAR'B'F
JPAN
BRAR'B'F
.
JPAN
BRAR'K'F
JPAN
MDAR'A'F
JPLS
MDAR
MDAR'H'A' F
ARAR ' H 'F
JPLS
MDAR
JPAN
MDAR'X
JPLS
40 ! H
FNSWS
FNSWS
IC
START
FREEZ
TIMED
FBF
SPARE
RETRN
I
TMC:LR
FNSWIiS
1463
[READ FUNCTION SWITCHES
[READ FNS 1-15
[STORE FUNCTION SWITCH STATUS
[EXAMINE STATUS
[35(6) FIRST IN BR
[SET INITIAL CONDITIONS
[S5(1) FIRST IN AR
[START DYNAMICS FNSW 2
[S5(2) FIRST IN AR
[FREEZE DYNAMICS FNSW 3
[S5(3) FIRST IN AR
[DISPLAY CLOCK FNSIJ 4
[S5(4):' FIRST IN AR
[EXECUTE FRAME B' FRAME
[55(7) FIRST IN AR
[SPARE TIME DISPLAY FNSW 8
[85(12) FIRST IN AR
[RETURN TO CALLING PGRM FNSW 13
IN AR(29)
[S5(11)
[KILL TIME DISPLAYS FNSW 12
[CHECK FOR FAST MOVE
[FNSW 6. 7. 10,11, 14, 15
FMOVE
FBFFL
, 6
FRCNT
. 4
(+0
IF
F.
BY F,
MODE
[ADD UNTIL +0
[THEN FREEZE
RX'F
ARMD'N
ARMD
MDAR
JPAN 'I
NOOP
NOOP
JUMP
FREEZ:
RETRN:
KILL:
FBFFL
RE ADY
READY
FNS1.1
[EXECUTE REST OF SIMI
[IF DISPLAY IS NOT FROZEN
[ELSE PREVENT DYNAMIC: UPDATE
[AT THIS POINT IN SIMI AND
[AT END OF RDISC IN SIM2
A RX0 ' F
ARMD
JUMP
READY
STATS
[SET FREEZ MODE
[FREEZE IS READY
MD10 'H'F
MDAR'F
ARMD
ARMD
JUMP 'I
0
KILL
77755
77757
INIT
[RETURN TO THE MONITOR
'I
IL.JUMP
= +0
[ CH AN GE CLOCK:I( P I VOT
[CHANGE EOL PIVOT
[ RETURN Ti1 CALL I NiG PGRM
. -1
123
FMOVE:
FUP:
FDOWN
FNORT
FSOUT:
FEAST:
FWEST:
MDAR' A
ARAR' H'F
ARRS
JPLS
ARRS
JPLS
ARRS
JPLS
ARRS
JPLS
ARRS
JPLS
ARRS
JPLS
JUMP
MSK
1
FDOWN
1
FSOUT
3
FUP
1
FNORT
:3
FEAS1T
1
FWEST
STATS
[ENTER IF ANY FAST MOVE
(FUNCTION SWITCH IS ON
EFNSW
15
[FNSW
14
(FNSW
11
(FNSW
10
[FNSW
7
[FNSW
6
[INSURED RETURN
MDAR
MDAE
ARBR'F
MDAE'N
JPAN
MDAR
ARMD
JUMP
BRMD
JUMP
R
FRINC
[GET ALTITUDE 823
[ADD ALTITUDE INCREMENT
RLIM
, 4
RLIM
R
FFNSH
R
FFNSH
[SUBTRACT
MDAR
MDAE'N
ANAR
ARMD
JUMP
R
FRINC
ZERO
R
FFNSH
MDAR
MDAE
ARMD
JUMP
0
FHINC
Q
FFNSH
MDAR
MDAE'N
ARMD
JUMP
FH I NIC
MAX ALTITUDE
[IF GRT THAN LIMIT
[STORE LIMIT
[IF LESS THAN LIMIT
(STORE NEW ALTITUDE
[SUBTRACT R INCREMENT
[IF NEGATIVE SET = 0
[ADD HORIZ
[SUBTRACT
INCREMENT
INCREMENT
FFNSH
MDAR
MDAE
ARMD
JUMP
P
FHINC
P
FFNSH
MDAR
MDAE'N
ARMD
JUMP
P
FH I NC
P
FFNSH
[ADD
INCREMENT
ESUBTRACT
INCREMENT
124
FMOVE I
FUP I
FDOWN'
FNORTI
FSOUTI
FEAST
FWEST
MDAR 'A
ARAR'H'F
ARRS
JPLS
ARRS
JPLS
ARRS
JPLS
ARRS
JPLS
ARRS
JPLS
ARRS
JPLS
JUMP
MSK
1
FDOWN
1
FSOUT
3
FUP
1
FNORT
3
FEAST
1
FWEST
STATS
CENTER IF ANY FAST MOVE
[FUNCTION SWITCH IS ON
[FNSW 15
CFNSW 14
CFNSW 11
EFNSW 10
EFNSW
7
CFNSW 6
CINSURED RETURN
MDAR
MDAE
ARBR'F
MDAE'N
JPAN
MDAR
ARMD
JUMP
BRMD
JUMP
R
FRINC
[GET ALTITUDE 923
CADD ALTITUDE INCREMENT
RLIM
ESUBTRACT MAX ALTITUDE
MDAR
MDAE'N
ANAR
ARMD
JUMP
R
FRINC
ZERO
R
FFNSH
MDAR
MDAE
ARMD
JUMP
0
FHINC
0
FFNSH
MDA P
MDAE'N
ARMD
JUMP
0
MDAR
MDAE
ARMD
JUMP
P
MDAR
MDAE 'N
ARMD
JUMP
P
FHINC
' 4
RLIM
R
FFNSH
R
FFNSH
FHINC
CIF GRT THAN LIMIT
ESTORE LIMIT
[IF LESS THAN LIMIT
[STORE NEW ALTITUDE
ESUBTRACT R INCREMENT
CIF NEGAT IVE SET = 0
CADD HORI2 INCREMENT
[SUBTRACT
INCREMENT
0
FFNSH
FHINC
CADD
INCREMENT
P
FFNSH
P
FFNSH
[ SUBT RAC T INCREMENT
125
FFNSH:
MDAR
JPAN'I
MDAR
ARMD
MDAR
ARMD
JPSR
JUMP
ARXO'F
ARMD
JUMP
ARXO'F
ARMD'N
JUMP
ARXO'F
ARMD 'N
ARMD'N
ARMD
JUMP
READY
FNSW
P
$XP
Q
$YP
$INIFI
STATS
START:
ARMD'O
JUMPI'I
READY
FNSW
[START DYNAMICS
[READY = -
FBFI
MDAR'H
JPAN
MDAR'F'N
ARMD
ARMD'0
ARXO'F
ARMD
JUMP
0
0
FRCNT
STATS
2
FRCNT
READY
[IF NEG THEN ALREADY
[COUNTING SO DISREGARD
[COUNT ONE FRAME
FBFFL
STATS
[FLAG +0 FOR F,
TIMED:
SPARE:
TMCLR:
FBFFL:
FRCNT:
$CLCKF
STATS
$STIMF
STATS
$CLCKF
$SDISF
$STIMF
[READY = - IS DYNAMICS
[READY = + IS STATIC
[SO THAT MAP WILL
[INDICATE FAST MOVE
[CORRECT FLT INSTMTS
[FLAG TO DISPLAY
[CLOCK FROM "CRGD2"
[+0 TO DISPLAY
[FLAG TO DISPLAY SPARE
[TIME FROM "CRGD2"
[-0 TO DISPLAY
[TURN OFF CLOCK,
[STROBE TIME,
[AND SPARE TIME
STATS
[READY = -0
(UNFREEZE)
BY F,
126
RDISC:
EOFRD:
S6MD
MDAR'H
JPLS
JUMP
MDAR'A'F
JPLS
JPSR
JPSR
JPSR
JPSR
SSIX0
SSIX0
, 2
EOFRD
70000
CHKS6
SSCL
SCLUT
ACDIS
$S60 lip
MDAR
JPAN'I
JUMP
READY
RDISC
MDBR'B
MDAR'H
JPAN
MDAR
MDAR
MDAR
JUMP
MDAR
MDAR
BRAR'H'F
JPAN
ARMD'N
MDAR
ARMD
MDAR
ARMD
MDBR 'B
BRAR'F
MDAR'A'F
JPLS
JUMP
MDAR
ARMD'N
BRBR'B'F
ARX0 ' F
ARMD
BRAR'N'K'F
JPAN
ARMD'O
BRAR'H'F
JPAN
ARAR'B'F
JPAN
BRAR'F
MDAR'A'F
JPLS
JUMP'I I
SSIX0
SSIX0
NAVI
SVROP
SVROP1
SVROQ.
' 5
$PVORPJ
$PVORQ;
ACDIS:
NAVI
DNEDS:
ACDI1
RDIS1:
ADFSS
$ADFFL
SVR2P
$ADFP
SVR2Q
$ADFQ
SSIX0
4000
, 2
ACDI 1
DAILE
ABIAS
GFLG
. 2
GFLG
TRIMU
[READ DISCREAT CHANNELS
[SAMPLE SOURCE 6
[PREVENT TRANSIENTS BY
[IGNORING IF L,H. IS
[ALL O'S (GEAR UP/DOWN)
[IF NOT REGISTER 0
[OF SOURCE 6 GO CHECK
ESET TSD SCALE
[CHOOSE DATA FOR DISPLAY
[AIRCRAFT EQUIP DISCRETES
[DISCRETE 4D INPUTS
[IF DISPLAY IS FROZEN
[STOP SIM2 SEQUENCE HERE
[ELSE DO DYNAMICS
[READ AIRCRAFT INPUTS
[56(1) FIRST IN BR
[S6(15) IST IN AR
[- IF CAPTAINS SW IN VOR
[OUTER MARKER ON
$SVORP
ARMD
$SVORQ
ARMD
[OUTER MARKER ON 4R HAS BEEN SELECTED
$SVORP
ARMD
$SVORQ
ARMD
[SAME STATION AS HSI HAS BEEN SELECTED
[- IF 1ST OFF SW IN VOR
[- GARBAGE FOR 1ST OFF
[SW IN ADF CAUSING
[DISPLAY$OF LYNNFIELD
[BEACON ON FAT NEEDLE
[RETURN FROM ADFSS
[36(2) IST IN AR
[MASK FOR BIT 19
[IN BIT 18 OF AR
[GIVE CURRENT AILERON
[TO ABIAS
[36(2) IST IN BR
[+ 0 IF UP
[36(8) IST IN AR
[IF GEAR DOWN GFLG
[S6(17) 1ST IN AR
[TRIM NOSE UP
[S6(18) IST IN AR
=
-0
TRIMD
4000
STROT
ACDIS
[86(2) STILL IST IN BR
[MASK FOR S6(20)
[SET TIME TO BE STROBED
127
RDISC:
EOFRD:
S6MD
MDAR'H
JPLS
JUMP
MDAR'A'F
JPLS
JPSR
JPSR
JPSR
JPSR
SSIX0
SSIX0
. 2
EOFRD
70000
CHKS6
SSCL
SCLUT
ACDIS
$S60OP
MDAR
JPAN'I
JUMP
READY
RDISC
MDBR'B
MDAR'H
JPAN
MDAR
MDAR
MDAR
JUMP
MDAR
MDAR
BRAR'H'F
JPAN
ARMD'N
MDAR
ARMD
MDAR
ARMD
MDBR'B
BRAR'F
MDAR'A'F
JPLS
JUMP
MDAR
ARMD'N
BRBR'B'F
ARXO'F
ARMD
BRAR'N'K'F
JPAN
ARMD'O
BRAR'H'F
JPAN
ARAR'B'F
JPAN
BRAR'F
MDAR'A'F
JPL S
JUMP 'I
SSIX0
SSIX0
NAV I
SVROP
SVROP;
SVRO 0
, 5
$PVORP;
$PVORQ;
ACDIS:
NAV1:
DNEDS
ACDI1:
RDIS1:
ADFSS
$ADFFL
SVR2P
$ADFP
SVR2Q
$ADFQ
SS1 1
4000
, 2
ACDI1
DA ILE
ABIAS
GFLG
[READ DISCREAT CHANNELS
[SAMPLE SOURCE 6
[PREVENT TRANSIENTS BY
[-IGNORING IF L,H, IS
CALL O'S (GEAR UP/DOWN)
(IF NOT REGISTER 0
[OF SOURCE 6 GO CHECK
[SET TSD SCALE
[CHOOSE DATA FOR DISPLAY
(AIRCRAFT EQUIP DISCRETES
[DISCRETE 4D INPUTS
[IF DISPLAY IS FROZEN
[STOP SIM2 SEQUENCE HERE
[ELSE DO DYNAMICS
[READ AIRCRAFT INPUTS
(36(1) FIRST IN BR
(S6(15) IST IN AR
[- IF CAPTAINS SW IN VOR
[OUTER MARKER ON
$SVORP
ARMD
$SVORQ
ARMD
[OUTER MARKER ON 4R HAS BEEN SELECTED
$SVORP
ARMD
$SVORQ
ARMD
[SAME STATION AS HSI HAS BEEN SELECTED
[- IF IST OFF SW IN VOR
[- GARBAGE FOR 1ST OFF
[SW IN ADF CAUSING
(DISPLAY$OF LYNNFIELD
[BEACON ON FAT NEEDLE
[RETURN FROM ADFSS
[S6(2) IST IN AR
[MASK FOR BIT 19
[IN BIT 18 OF AR
[GIVE CURRENT AILERON
[TO ABIAS
[S6(2) 1ST IN BR
[+
0
IF
(36(8)
, 2
GFLG
TRIMU
UP
IST IN AR
[IF GEAR DOWN GFLG = -0
(36(17) IST IN AR
[TRIM NOSE UP
[36(18) 1ST IN AR
TRIMD
4000
STROT
ACDIS
[36(2) STILL 1ST IN BR
[MASK FOR S6(20)
[SET TIME TO BE STROBED
128
GDM
[ILS - 4R
BOS
SMK00=2454; SMK0t=2445;
SMK10=3203;
[
PVD
HTO
ALB
SMK02=2305; SMK20=2605;
SMK22=2162
PYRSS:
$PVRFL
ARMD'O
SSIX1
MDBR'H
3777
MDBR'A'F
IREPEAT
NN,(00,01,10,11,02,20,22)
BRAR'F
SMK\NNN
MDXO'F
JPLS
, 2
PVR\NN
JUMP
ENDI
ARXO'F
$PVRFL
ARMD
PVRSS
JUMP 'I
PVRO0:
VRPO0;
MDAR
VRQOO
MDAR
$HSIS
MDAR
$APPRM
JSAN
JUMP 'I
PVRSS
IREPEAT
PVR\NN:
ENDI
ADFSS:
IREPEAT
NN, (01 10, 11,02,20,22)
VRP\NN
MDAR
VRQxNN.
MDAR
$HSIS
MDAR'N
JSAN
$VORLM
JUMP 'I
PVRSS
ARMD ''O
MDBR
MDBR'A'F
NN (00,01,
BRAR'F
MDX0' ' F
JPLS
JUMP
$ADFFL
SSIX1
3777(
10,11 ,02, 20. 22)
SMK \NN
, 2
ADF\NN
HTM
SMK11=1051
[PRIMARY VOR STATION SELECTION
[COMPARE EACH MASK TO
[SAMPLED FREQ SETTING
ARMD
ARMD
[SET HSI SENSITIVITY
ARMD
ARMD
IREPEAT
ADF\NN:
ENDI
NN. (00..01,
MDiR
MDAR
JUMP
[USE SAME MASKS AS PVRSS
$ADFFL
DNEDS
10,11, 02.20,22)
VRP\NN:N
VRQ'NN:'
DNEDS
$PVORP
$PVORQ
[DOUBLE NEEDLE STATION SELECTION ON NAV2
[REGISTER 1 FOR COMM/NAV
ENDI
ARXO'F
ARMD
JUMP
$PVORP
$PVORQ
ARMD
ARMD
129
MDAR'N
MDAS'F
ARMD'N
JUMP
MDAR
MDAS'F
ARMD
JUMP
ARXO'F
ARMD
JUMP 'I
EBIAS
TRINC
EBIAS
RDIS1
EBIAS
TRINC
EBIAS
RDISI
$STRBF
ACDIS
(EBIAS ESTABLISHED
[INITIALLY IN INIT
[SET STROBE FLAG
[FOR COMPUTING
[STROBE DISPLAY
VRPOO
VRPO 1:
VRP10:
VRP11
VRP02:
VRP20 :
VRP22:
166277;
-195520.;
177700;
40000.;
-110908.;
-416616.;
-643350.;
VRQ00
VRQ0 1:
VRQ10
VRQ1 1:
VRQ02:
VRQ20 1
VRQ22:
116300
180140,
116300
-62345.
-153054.
-383421.
334342,
(ILS
[GDM
[SOS
[HTM
SVROP:
SVRIP:
SVR2P:
SVR3P:
122400;
777716400;
237660;
7920.;
SVROQ:
SVR1iQ:
SVR2Q:
SVR3Q:
33076
343720
211120
-31680.
(SO
[BE
[SEW
CHKS6:
MDAR'K
MDAR'A'F
ARRS
ARBR'F
MDAR' L;
BRAS'F
ARIR'F
JUMP
SSIX0O
70
3
[S6(0-2) NOW IN AR(24-26)
[EXTRACT S6(0--2)
[PUT IN AR(27-29)
[ADD REGISTER NUMGER
CHK6L
[TO GET LOCATION CHK6L
[EXECUTE SUBROUTINE
TRIMD:
TRINU
STROT:
CHK6L:
SET60
SET61;
KILL
[TRIM STABILIZER BY
[CHANGING ELEVATOR POSITION
(ASSOCIATED WITH NEUTRAL
[COLUMN POSITION
JPSR'I
(PVD
[HTO
[ALB
[OWD
EOFRD
SET62;
SET63;
SET60:
JUMP' I
SET 60
MDAR
ARMD
JPSR
JUMP ' I
SSIX0)
SSIX1
PVRSS
SET61
MDAR
ARMD
JPSR
JUMP' I
ssIX0
SSIX2
$S62WP
SET62
MDAR
ARMD
JPSR
JUMP ' I
SSIXO
SSIX3
$S63WP
SET63
[REGISTER 0, ETC.
KILL
KILL;
SE T64;
[ERROR HAS OCCURRED
[ERROR HAS OCCURRED
SET61:
SET62:
SET63:
-----------------------
[CHANGE VOR STATION
[SELECTED
130
SET64:
,
MDAR
ARMD
JUMP 'I
SSIX0
SSIX4
SET64
MDAR'H
MDAR'A
MDAS'F
ARMD
ARMD
JUMP 'I
SSI :Io
SEVEN
1
SCALE
$SSC
SSCL
MDAR'H'N
ARBR'F
MDAR'A'F
JPLS
ARXO'F
JUMP
MDAR'LU
ARMD
BRAR'F
MDAR'A'F
JPLS
ARXO'F
JUMP
MDAR'L;
ARMD
BRAR'F
MDAR'A'F
JPLS
ARXO'F
JUMP
MDAR'LU
ARMD
BRAR'F
MDAR'A'F
JPLS
ARXO'F
JUMP
MDAR'L;
ARMD
JUMP 'I
SSIX0
SSCL:
SCLUT :
1000
. 3
[SOURCE 6 FOR RANGE
[SET CLUTTER LEVEL, OR
CA/N DATA FOR WAYPOINTS
[ID MASK
. 3
JUMP
$TDP
4000
[ALTITUDE MASK
JUMP
$TAP
$TDS
2000
.3
[SPEED
.3
JUMP
$TSP
400
.3
.3
JUMP
$TTP
SCLUT
MASK
$TDT
[TRACER MASK
$TD2
131
IC:
ICL1;
ICL2:
MDAR'H'X
JPAN
MDAR'F
ARMD'N
ARXO'F
ARMD
ARMD'N
ARMD
ARMD
ARMD
ARMD
ARMD
ARMD
ARMD
ARMD
ARMD
MDAR'I'X
JPAN
ARMD
MDBR'H'F
ARLS
BRMD
ARMD
MDAR'I'X
ARMD
ARMD
MDAR'I'X
ARMD
ARMD
MDAR'I'X
ARMD
ARMD
MDAR'I'X
ARMD
MDAR'I'X
ARMD
MDAR'I'X
ARMD
MDAR'I'X
ARMD
MDAR'I'X
ARMD
TTIME
$SDISF
RSLD
PRATE
QRATE
RRATE
VZ
GFLG
VB
ATCNT
READY
ICPTR
ICL2
R
17777
7
RCLD
RB16
ICPTR
P
$XP
ICPTR
0
$YP
ICPTR
UB
VT
ICPTR
WB
ICPTR
ESLD
ICPTR
ECLD
ICPTR
YSLD
ICPTR
YCLD
JPSR
MDAR
JPLS
JPSR
JPSR
JUMP
MDAR'F
ARMD
JUMP
ATMOS
ATCNT
-2
AERO
$INIFI
STATS
ICLST-1
ICPTR
ICL1
ICCNT
STATS
15
ICCNT
[COUNT ONE SECOND BEFORE
[ENTERING NEXT INITIAL CONDITION
[LEVEL FLIGHT INITIAL CONDITIONS
[ZERO CLOCK
[AND KILL STROBE DISPLAY
[SIN PHI = 0 (WINGS LEVEL)
CANGULAR VELOCITIES
[+0 FOR GEAR UP
[Y BODY VELOCITY
[FORCE ATMOS TO DO ATMO1
[FREEZE ON RETURN
[LAST ENTRY LEG
[INITIAL ALTITUDE
B23
(COS PHI = +1
[ALTITUDE B16
CINITIAL X POSITION 823
[IN FEET
[FOR "MMAP2"
[INITIAL Y POSITION B23
(INITIAL X BODY
[TO PREVENT DIV
[TOTAL VELOCITY
[INITIAL Z BODY
[SIN THETA
VELOCITY
BY ZERO
THE SAME
VELOCITY
(PITCH)
[COS THETA
[SIN PSI
[COS
(HEADING)
PSI
[INITIALIZE ATMOSPHERE
(RECALL UNTIL COMPLETE
[INITIALIZE A IRSPEED
[INITIALIZE FLIGHT INSTRUMENTS
[RETURN TO FUNCTION SWITCHES
[RECYCLE
I.
CS
132
ICCNT:
0
ICPTR:
ICLST-1
[62 N.M. SW, OF HAMPTON AT .82 MACH (476 KTAS) (289 KIAS)
[ALTITUDE B23
ICLST:
35000. iK
[X POSITION B23
-720215, 1K
[Y POSITION 823
-611023, !K
CX BODY VELOCITY 804 FT/SEC B10
31100 !H
(2 BODY VELOCITY B9
77471 !H
[SIN PITCH 61
10! H
[COS PITCH B1
20000 !H
[SIN HEADING BI
14616! H
11501 H
[COS HEADING 81
(17 N.M, W OF ALBANY AT .82 MACH (494 KTAS) (359 KIAS)
25000.!K
-742359.!K
364611,1K
[835 FT/SEC
32060!H
77471!H
10!H
20000 !H
17232!H
732441H
[10 N.MI, W. OF GRISWOLDVILLE (SHORT TEST CASE)
15000., K
-445793. !K
273942.!K
14360!H
13111H
711!H
17763!H
172321H
73244!H
(20 NM. S.W. OF MILLIS AT 236 KTAS (220 KIAS)
6000, !K
-142655.!K
--88683.!K
(400 FT/SEC
14360!H
1311! H
711!H
1776: 3!H
15442! H
10:364! H
[ASSURED RECYCLE
-0
133
[FOLLOWING SUBROUTINE EMPLOYS THE ANALOG - DIGITAL CONVERTER
[TO SAMPLE ANALOG CONTROL INPUTS FROM THE COCKPIT
KIAS L.T. 188
[SPOILER BLOWDOWN: MAX SPOILER = 60 DEG
60 - .283(KIAS - 188) G.T. 188
[
VCD1:
NODEC:
FPRI
MDG07'L;
NOOP
MD07'L;
MDAR'B
UPRI
MDAE'N'H'F
JPAN
ARAR'H'F
MPYI
NOOP
MDAE'H'N'F
ARBR'N'F
76560 1H
JPAN
BRMD'H
JUMP
S5MD
FPRI
MD07'L;
NOOP
MDAR'N'H'F
76560 IH
MD07'LU
ANAR
UPRI
ARAR'H'F
MPYI
MDBR'H
ARMD'B
MDAR'B
JPAN
ARMD
JUMP
BRMD
FPRI
MD07'L;
MDAR'N'H
MDBR
S5AS'F
MD07'LU
UPRI
JPAN
BRAR'F
MDAE
ARMD
JUMP
11 H
NOOP
0
10
KIAS
[TURN OFF MPX 8-15
13600
NODEC
(188 KTS 89
30446
E.283(1
12135
[ANTICIPATED MAX SPOILER
[SAMPLE MPX 3 (SPEED BRAKE)
[KIAS TO S'9
DEG SPOILER) B-9R
[S5AE'H'F
NODEC
DSPOL
. 2
DSPOL
[STORE DECREASED MAX BOR
[STORE ACTUAL SPOILER
240
[MPX 4-7 (THROTTLES)
11574
[EXPECTED IDLE THROTTLE
[S5AE'H'F
[TURN OFF MPX 0-7
0
ZERO
25012
FS
DTHRO
DTHRO
'3
DTHRO
. 2
DTHRO
11H 1
DFLAP
FRATE
1!H 2
. 5
DFLAP
DFLAP
. 4
[INVERSE EXPECTED MAX B2
[I.E. NORMALIZE
[STORE TEMP 81
[RECALL BO
[IF L.T. 1
[STORE B0
[ELSE STORE 1 BO
[SAMPLE MPX 8 (FLAPS)
[CURRENT FLAP POSITION
[EXTEND/RETRACT RATE
[COMMANDED FLAP POSITION
[SAMPLE MPX 9 (ELEVATOR)
[IF COMMAND FLAP POSITION
[G.T. CURRENT FLAP POSITION
[ADD INCREMENT TO CURRENT
[ELSE SUBTRACT INCREMENT
[FROM CURRENT
134
BRAR'N'F
MDAE
ARMD
MDAR'L
EBIAS:
0
S5AS'F
FPRI
MD07'L;
ARMD
MDAR'L
ABIAS:
0
SSAS'N'F
MD07'LU
ARMD
UPRI
MDAR'L
RUDB:
0
S5AS'N'F
ARMD
JUMP'I I
[FOLLOWING SAMPLES CCJURSE
VCD2:
FPRI
MD07'LU
NOOPJ'
MD07'L
NOOP;
DFLAP
DFLAP
[COMPUTED DFLAP BO
[ELEVATOR BIAS FROM INIT
[HAS CONVENTIONAL SIGN
1!H 4
DELEV
i!H 10
DAILE
[SAMPLE MPX 10 (AILERON)
[AILERON BIAS FROM INIT
[CHANGE TO CONVENTIONAL SIGN
[SAMPLE MPX 11 (RUDDER)
[RUDDER BIAS
[CHANGE TO CONVENTIONAL SIGN
DRUDD
VCD1
SETS HEADING BUG AND SPEED SET BUG
1!H
NOOP
2!H 10
NOOP
[TURN OFF MPX 8-15
14400
2!H 20
$SPSET
[400 KTS B10
[MPX 20 VERT GRADIENT
[SPEED BUG SETTING B10
$PTCHT
2!H
NOOP
1!H 20
NOOP
[PITCH TRIM FOR ADI
[TURN OFF MPX 16-23
[MPX 19 SPEED BUG
SSAR'F
MPYI
MDO7'L;
ARMD
NOOP
S5MD
MD07'L;
NOOP;
MD07'LU
NOOP;
[MPX 12 HDING SIN
S5AR'H'N'F
MD07'L
NOOP,
I!H 40
NOOP
[MPX 13 HDING COS
1!H200
[MPX
S5BR'H'F
MD07'LU
UPRI
JPSR
15 COURSE COS
$SCINV
S5BR'H'F
FPRI
MD07'L
ARMD
NOOP
UPRI
SSAR'H'N'F
JPSR
ARMD
JUMPI I
1 H100
$DHANG
$SCINV
$PVORA
VCD 2
[MPX 14 COURSE SIN
135
AERO
.
[AIRSPEED AND ALPHA CALC.
[FOLLOWING IS AN APPROXIMATE SQ ROOT SEE KEMP'S THESIS
[VT(N) = 1/2 (VT(N-1) + (U*U + V*V + W*W)/VT(N-1) )
MDAR'H
MPYU
NOOP
ARMD
MDAR'H
MPYU
MDBR
ARRS
ARMD
BRAR'H'F
MPYU
MDBR
ARRS
ARMD
BRAE'F
MDAE
ARBR'F
MDAE'N
ANIR
ARLS
NOOP
MDAE'N
ARAR'N'F
JPAN
BRAR'F
ARRS
DIVU
NOOP
ARBR'H'F
MDAR
ARRS
BRAE'F
ARMD
ARAR'H'F
AERO1:
MPYU
NOOP
ARMD
ULSQ
V8
VB
We
2
VBSQ
WB
UBSQ
2
WBSQ
VBSQ
VSQR
NEGAT
3
VSQR
SQRRT
1
VT
MDAR
DIVU
MDBR
ARAR'H'F
ARMD
ARRS
CVB FROM FORCE TO B9R
[SQUARED B18
[STORE B20
[WB TO 89R
(SQUARED B18
(STORE B20
[NEW VSQR=U**2+V**2+
[W**2 TO BR B20
[IF OLD VSQR G.T. NEW
[THEN DV= -(NEW-OLD)
[ELSE DV = NEW-OLD
[SUBTRACT 1/8TH OLD
[IF DV L.T. 1/8TH OLD
[THEN TAKE SQR RT OF NEW
[ELSE DIVIDE (NEW * 1/2)
[BY OLD
[QUOTIENT BlOR
[BR= .5(VSQR'VT) AS B10
VT
1
[VT TIMES 1/2
CVT/2 + (VSQR/VT)/2
[NEW VT AS 810
VT
VT
VSQR
[RETURN FROM SQRRT
[NOTE: IF SQRRT USED
[IT UPDATES VT
ASSUMES COSB = 1
[SINA = WB/VT = ALPHA
[COSA = UB/VT
(SINB = VB/VT = BETA
(COSB = 1 - BETA SQRED/2
ATACK:
[UB FROM FORCE TO B1OR
[SQUARED B20
UB
UB
WB
VT
US
ALPHA
2
[WB AS 89
[DIVIDE BT VT
[QUOTIENT TO B-2
[ANGLE OF ATTACK B-1
136
ARMD
BRAR'F
ARRS
DIVU
MDBR
ARAR'H'F
ARMD
BRAR'F
DIVU
MDBR
ARAR'H'F
ARMD
ARRS
ARMD
ARAR'H'F
MPYU
NOOP
MDAE'H'F
ARMD'N
BRAR'F
ARRS
DIVU'
NOOP
ARMD'H
MPYU
NOOP
ARMD
JUMP'I
SQRRT:
BRAR'F
JPSR
ARMD'H
JUMP
SINA
(UB TO B1OR
1
VT
VB
[DIVIDE BY VT B10
COSA
[RESULT TO 80
(COS ALPHA
(YB AS 69
VT
VT
BETA
2
SINB
[QUOTIENT TO B-2
(BETA B-1
[SIN BETA
81
SINB
[BETA SQRED B2/2'= B1
57777
COSB
1
SPDSN
(-1 AS 61
[COSB B1
[TRUE VELOCITY FT/SEC
[TO B11
[SPEED OF SOUND 811
MACH
M2IAS
[MACH 60
[CONVERSION FROM ATMOS
KIAS
AERO
[INDICATED AIRSPED 810
[NEW VSQR IN BR
$SQRT
VT
AERO1
(UPDATE
VT
137
(-LIFT) + THRST)
(CACB(-DRAG) -CASB(YAERO) -SA
EXBM = (1/MASS)
(-DRAG) +CB (YAERO) + 0
(SB
[YBM = (1/MASS)
)
(-LIFT)
(SACB(-DRAG) -SASB(YAERO) +CA
(ZBM = (1/MASS)
[WIND TO BODY AXES
,
WTOB:
[NEC DRAG TO B17R
DRAG
MDAR'N'H
(TIMES COS BETA 81
COSB
MPYU
NOOP
CHOLD C8*DRAG B18
ARBR'F
(YAW FORCES 816
YAERO
MDAR'N'H
[TIMES SIN BETA 61
SINE
MPYU
NOOP
1
ARRS
818
[-CB*DRAG-SB*YAERO
BRAE'F
[USING BR SAVES 1 MI.SEC'
ARBR'F
(NEG DRAG TO B17R
DRAG
MDAR'H'N
[TIMES SIN BETA B1
SINS
MPYU
B18
[STORE ABOVE SCALAR
DTEM
BRMD
[-SB*DRAG
ARBR'F
YAERO
MDAR'H
[TIMES COS BETA
COsB
MPYU
NOOP
ARRS
1
B18
[-SB*DRAG+CB*YAERO
BRAE'F
[DEFINED MASS B13R
MASS
DIVI
[QUOTIENT 85R
NOOP
ARAR'H'F
4
ARRS
[TO 89
ARBR'F
B18R
[RECALL ABOVE SCALAR
DTEM
MDAR'H
[TIMES COS ALPHA 81
COSA
MPYU
[(-SB*DRAG+CB*YAERO)/M 84
YBM
BRMD
[PRODUCT TO B22
3
ARRS
[CAC-CB*DRAG-SB*YAERO)
ARBR'F
[LIFT FROM AERO TO B21R
LIFT
MDAR'H
[TIMES SIN ALPHA
SINA
MPYU
NOOP
[(CA(-CB*DRAB-SB*YAERO)+
BRAE'F
[SA*LIFT + THRST) B22
THRST
MDAE
[DIVIDED BY MASS 813R
MASS
DIVI
NOOP
[QUOTIENT TO 85
ARBR 'H' F
[SAME SCALAR
DTEM
MDAR'H
SINA
MPYU
[STORE AS 88
XBM
BRMD'B
[PRODUCT TO B22
3
ARRS
ARBR'F
(NEG LIFT TO B21R
LIFT
MDAR'N'H
[TIMES COS ALPHA
COSA
MPYU
[PRODUCT B22
NOOP
B22
[ADD SA(SCALAR)
BRAE'F
[(SA(-CB*DRAG-SB*YAERO)
MASS
DIVI
[-CA*LIFT)/MASS
NOOP
[STORE 89
ZBM
ARMD'H
WTOB
JUMP'I
822
138
[PDOT
[QDOT
ERDOT
EQPM:
=
=
L/IX
M/IY
N/IZ
-RQ(IZ-IY)/IX +PQ IX2/IX
-PR(IX-IZ)/IY -(PSQR-RSQR)IXZ/IY
-PQ(IY-IX)/IZ
-RQ IXZ/IZ
.
MDAR'H
MP'YU
NOOP
ARBR'H'F
BRAR'F
MPYI
BRMD'N
ARRS
ARBR'F
MDAR'H'N
MPYU
NOOP
ARAR'H'F
ARMD
MPYI
NOOP
BRAE'F
ARRS
MDAE
PRATE
QRATE
IXZIX
PQ
2
RRATE
QRATE
RQ
IZMIY
3
LMOM
[MOMENT EQUATIONS
[OLD P TO BOR
[TIMES OLD Q BO
tPRODUCT IS S0
LMOVE MOST SIGNI[FIGANT TO R.H. BtR
[DEFINED QUOTIENT
[STORE PQ PRODUCT
ARBR'F
MDAE'N
BRAE'B'F
ARAR'H'F
MPYI
NOOP
ARRS
MDAE
ARMD
MDAR'H
MPYU
BRMD
ARBR'N'F
MDAR'H
MPYU
NOOP
ARRS
BRAE'F
ARAR'H'F
MPYI
NOOP
ARRS
ARBR'F
MDAR'H'N
MPYU
NOOP
ARAR'H'F
B2
[HOLD PQ*IXZIX
[- OLD R TO B-iR
[TIMES OLD Q B0
[MOST SIGNIFIGANT
[STORED NEG AS B-1R
[DEFINED BOR
[PRODUCT B-1
[ADD -RQ(IZ-IY)/IX B-1
[TO PQ*IXZ/IX + L/IX B2
[INTEGRATION RULE: X(N)=X(N-1) + H/2 (3XDOT(N) - XDOT(N-1)
INTPD:
B-3R
NEG.
)
PDOT
[HOLD NEW PDOT B2
[SUBTRACT OLD PDOT 82
[ADD TWO MORE NEW PDOTS
DT15
[(DELTA T)/2 B-4R
2
PRATE
PRANW
PRATE
PRATE
PDOT
RRATE
RRATE
2
IXZIY
[ADD OLD P 80
[STORE
[OLD P TO BOR
[SQUARE IT BO
[UPDATE PDOT B2
[HOLD - P SQUARED BC
[OLD R TO B-iR
[SQUARE IT B-2
[ADD R SQUARED
[AS BC
[TO -P SQUARED 80
[RESULT TO BOR
[TIMES QUOTIENT IXZ/IY
4
PRATE
RRATE
[HOLD RESULT 81
[- OLD P TO BOR
[TIMES OLD R B-1
[PRODUCT IS B-1
[TO B-iR
139
MPYI
NOOP
ARRS
IXMIZ
2
[ADD (-P**2+R**2)IXZ/IY
BRAE'F
MDAE
INTOR:
INTRR:
ARBR'F
MDAE'N
BRAE'B'F
ARAR'H'F
MPYI
NOOP
ARRS
MDAE
ARMD
MDAR
MPYI
BRMD
ARRS
ARBR'F
MDAR
MPYI
NOOP
ARRS
BRAE'F
MDAE
ARBR'F
MDAE'N
BRAE'B'F
ARAR'H'F
MPYI
BRMD
ARRS
MDAE
ARMD
MDAR
ARMD
JUMP' I
OVERF:
,
ARS:
BRS:
ARMD
MDAR'L
MD1O'H'F
ARMD
ARIR'F
BRMD
JUMP
JUMP
0
0
[QUOTIENT (IX-IZ)/IY
MM04
QDOT
[HOLD FOR INTEGRATION
[SUBTRACT OLD QDOT BI
[ADD TWO MORE NEW ODOTS
DT15
[DEFINED AS B-4R
3
QRATE
QRATE
PQ
IYMIX
QDOT
2
[ADD OLD 0
[UPDATE Q
[SAVED ABOVE AS NEG BOR
[QUOTIENT (IY-IX)/IZ B-2R
[UPDATE Q DOT
RQ
IXZIZ
[HOLD PQ(IY-IX)/IZ Bo
[SAVED ABOVE AS NEG B-IR
[QUOTIENT IXZ/I2 B-4R
5
NMOM
RDOT
DT15
RDOT
3
RRATE
RRATE
PRANW
PRATE
EQMM
ARS
[ADD PQ(IY-IX)/IZ 80
[ADD N/IZ B0
[HOLD FOR INTEGRATION
[SUBTRACT OLD RDOT 80
[ADD TWO MORE RDOTS
[UPDATE RDOT
[ADD OLD R B-1
[UPDATE R
[NOW YOU CAN UPDATE
[P AS WELL
[JUMP HERE ON OVERFLOW
[SAVE AR
[STOP
[7756 CLOCK AND DISPLAYS
BRS
IMON9
[SAVE BR
[RETURN TO MONITOR
140
-SE
[UDOT
[VDOT = G ECRS
ECRC
[WDOT
G=20063
0
-R
Q
R -Q
P
0
-P 0
INTUD:
+
XBM
YBM
ZBM
[GRAVITATIONAL ACC. B6R
G
ECLD
[FORCE EQUATIONS
[GRAVITY B6R
[TIMES COS THETA B1
RSLD
[RESULT TO 17
[RESULT TO B7R
[TIMES SIN PHI 81
FORCE:
MDAR'F
MPYU
NOOP
ARBR'F
BRAR'H'F
MPYU
NOOP
ARRS
ARMD
BRAR'H'F
MPYU
MDBR
ARRS
ARMD
BRAR'H'F
MPYU
NOOP
MDAE
ARRS
ARBR'F
MDAR'N'H
MPYU
NOOP
BRAE'F
ARBR'F
MDAR'N'F
MPYU
NOOP
ARRS
BRAE'F
ARLS
NOOP
ARBR'F
MDAE'N
BRAE'F'B
ARAR'H'F
MPYI
NOOP
ARRS
MDAE
ARMD
MDAR'N'H
MPYU
BRMD
MDAE
ARBR'F
MDAR'H
MPYU
UB
VS
WB
1
GECRS
RCLD
RRATE
1
GECRC
VB
[TEMP STORE 89
[G*COS THETA 87R
[TIMES COS PHI
[R FROM S/R EQMM B-1
[G*CTHETA*CPHI B9
[RRATE TO B-IR
[Y VELOCITY COMP B9
XBM
I
[FROM WTOB S/R 88
ORATE
WB
ENEGQ FROM EQ.MM TO BOR
[2 VELOCITY COMP 89
[A = -R*VB-Q*WB+XBM B9
G
ESLD
[NEG GRAVITY
[TIMES SIN THETA 81
2
[B
= G*STHETA + A
3
UDOT
[SUBTRACT OLD UDOT 86
[ADD TWO MORE NEW UDOTS
DT15
[DELTA T OVER 2 B-4R
8.
Us
UBN
RRATE
UB
UDOT
YBM
PRATE
We
[ADD X COMP 810
[STORE UNTIL END
[-R FROM EQMM S/R B-1
[TIMES X COMP B10
[UDOT = B
[ADD YBM FROM WTOB
[C = -R*UB + YBM
[P TO BOR
[TIMES 2 COMP B9
141
INTVD:
INTWD:
NOOP
BRAE'F
MDAE
ARLS
NOOP
ARBR'F
MDAE'N
BRAE'B'F
ARAR'H'F
MPY I
NOOP
ARRS
MDAE
ARMD
MDAR'H
MPYU
BRMD
ARBR'F'B
MDAR'N'H
MPYU
NOOP
BRAE'F
MDAE
MDAE
ARBR'F
MDAE'N
BRAE'B'F
ARAR'H'F
MPYI
BRMD
ARRS
MDAE
ARMD
MDAR
ARMD
MDAR
ARMD
JUMP ' I
GECRS
2
[ADD C AS B9
[ADD G EFFECT
VDOT
ED = P*WB+GECRS+C
[SUBTRACT OLD VDOT B7
[ADD TWO MORE NEW VDOTS
DT15
[DELTA T FOR 15X'S /SEC
6
VB
VBN
QRATE
UB
VDOT
PRATE
VB
[STORE
EQ FROM EQMM 80
[TIMES X COMP B10
[UPDATE VDOT B7
[E = Q*UB
[NEG P TO BOR
[F = P*VB + E
ZBM
GECRC
WDOT
DT15
WDOT
4
WB
WB
UBN
UB
VBN
VB
FORCE
[G = GECRC+F+ZBM
[ADD NEG OLD WDOT
[ADD TWO NEW WDOTS
EWDOT = G
[UPDATE WB 89
[NOW CHANGE UB
[AND VB
142
[REQUIRES ANGULAR RATE IN RADIANS PER SECOND (82)
[PREVIOUS SINCOS
[SOLVES SIN(N+1) = SIN(N) + HR COS(N) - EMH SIN(N)
COS(N+1) = COS(N) - HR SIN(N) - EMH COS(N)
( &
(E = SIN2(N) + COS2(N) - 1
[WHERE R IS ANGULAR RATE, H IS TIME INCREMENT, M IS
[A CONSTANT SUCH THAT MH = 1/2, AND E IS ERROR TERM
SICOS:
.
IREPEAT NN,(R,EY)
MDAR'H
MPYU
NOOP
ARBR'F
MDAR'H
MPYU
NOOP
BRAE'F
MDAE'N'H'F
ARRS
NOOP
MPYI
NOOP
ARAR'H'F
ARBR'F
MPYU
NN\COS:
BRMD
MDAE'N
ARMD
MDAR
MDAE
ARAR'H'F
MPYI
NOOP
ARAR'H'F
ARMD
MPYU
NOOP
ARRS
MDAE
ARMD'N
NN\SIN:
MDAR
MPYU
NOOP
ARBR'F
MDAR
MPYUL
NOOP
ARRS
BRAE'N'F
MDAE
ARMD
NN\CLD
NN\CLD
(OLD COS TO BR
[SQUARED GIVES B2
NN\SLD
NN\SLD
[OLD SIN TO BIR
(SQUARED GIVES B2
ONEB2
15
[SUBRTRACT 1 AS B2
[SHIFT TO B15 OR BOR
17777
[M*H (JUST UNDER 1/2) BOR
NN\CLD
MEH
NN\CLD
NN\CNW
NN\RLD
NN\RNW
[FORM EMH COSCN) 81
[STORE ERROR TERM BOR
[SUBTRACT COS(N)
(TEMP STORAGE B1
[ANGULAR VELOCITY (N-1) B2
[AVGERAGED WITH AV.(N) 82
DT15
[DELTA T
NN'MHR
NN\SLD
[PRODUCT TO B-2R
[SAVE H*R B-2R
[FORM HR SIN(N) AS 81
2
NN\CNW
NN\CNW
(HR SIN(N) +(EMH COSCN)
[- COS(N) ) NEGATED 81
MEH
NN\SLD
[RECALL ERROR COEF.
[TIMES SIN(N)
NN\HR
NN\CLD
[RECALL HR AS B-2R
(HR COS(N)
/
2 FOR AVG.
B-4R
BOR
2
NN\SLD
NN\SLD
[HR COS(N) - EMH SIN(N)
[PLUS SIN(N)
[EQUALS SIN(N+1) 81
143
MDAR
ARMD
MDAR
ARMD
NN\CNW
NN\CLD
NN\RNW
NN\RLD
JUMP 'I
SICOS
[NOW UPDATE COS
[UPDATE ANGULAR RATE
[FOR EULER S/R
ENDI
IREPEAT NN,<REY)
ENTRY NN\CLD,NNNSLD,NN\CNI,NN\SNW, NW\RLD,NMtRNW
20000!H
NN\CLDi
NN\SLDi
0
200001H
NN\CNWI
NN\SNW:
0
NN\HR:
0
[IN RADIANS PER SECOND B2
0
NN\RLD:
[GARBAGE IN LHS
0
NN\RNW:
ENDI
0
MEH:
[COMPUTES EULER ANGLE RATES
[NEEDS PQ,R RATES
[GIVES RRERYR
(RATES MUST BE UNDER 1B1 WHEN ANGLES ARE 45 DEGREES
[RR
(ER
=
(YR
EULER:
RR:
1
0
0
SIN PHI TAN THETA
COS PHI
SIN PHI SEC THETA
MDAR'H
MPYU
NOOP
DI VU
NOOP
ARBR'F
MPYU
BRMD
ARRS
ARBR'F
MDAR'H
MPYU
NOOP
DIVU
NOOP
ARMD
MPYU
NOOP
ARRS
BRAE'F
ARBR'F
MDAR
ARRS
BRAE'F
ARBR'F
RSLD
ORATE
ECLD
COS PHI TAN THETA
- SIN PHI
COS PHI SEC THETA
P
Q
R
(OLD SIN PHI TO BIR
[TIMES Q BO
[PRODUCT 81
(OLD COS THETA 81
[QUOTIENT BOR
ESLD
RSECQ
[OLD SIN THETA B1
[(SPHI*Q)/CTHETA BOR
RCL D
RRATE
[PRODUCT
[OLD COS
[TIMES R
[PRODUCT
AS B2
PHI TO B1R
B-1
80
ECLD
RCECR
ESLD
[QUOTIENT B-IR
[(CPHI*R)/CTHETA B-1R
[OLD SIN THETA
[PRODUCT 80
2
PRATE
2
[(STHETA*RCECR)+
[(STHETA*RSECQ)
(P AS 80
[TO 82
[ADDED TO ABOVE
144
ER:
MDAR'N'H
MPYU
BRMD
ARRS
ARBR'F
MDAR'H
MPYU
NOOP
RSLD
RRATE
RRNW
1
COLD SIN PHI TO BIR
[TIMES R B-1
[STORE PHI DOT B2
RCLD
ORATE
COLD COS PHI TO BiR
[TIMES 0 80
BRAE'F
YR:
C(-SPHI*R)+(CPHI*Q)
ARRS
ARMD
1
ERNW
MDAR'H
ARRS
MDAE'H
ARRS
ARMD
JUMP'I
RCECR
1
RSECQ
2
YRNW
EULER
(NEW THETA DOT 82
[FROM ABOVE B-1R
[TO 80
(SHIFT TO 82
[NEW PSI DOT
[CONVERTS BODY VELOCITY COMPONENTS TO VEHICLE FRAME
UB
0
0
1
0 ES
EC
0
-YS
YC
CVX
VB
-RS
0 RC
0
1
0
0
YC
[VY = YS
WB
RC
0 RS
EC
-ES 0
1
0
0
[VZ
DIRCS:
ROLTP:
ELVTRI
MDAR'H
MPYU
NOOP
ARBR'F
MDAR'N'H
MPYU
NOOP
8RAE'F
ARBR'F
MDAR'H
MPYU
BRMD
ARBR'F
MDAR'H
MPYU
NOOP
BRAE'F
ARBR'F
BRAR'H'F
MPYU
BRMD
ARBR'F
MDAR'H'N
MPYU
NOOP
BRAE'F
ARLS
NOOP
yB
RCLD
CY COMPONENT TO B9R
[TIMES COS PHI B1
(PRODUCT B10
WB
RSLD
[NEG Z COMPONET TO 89R.
[TIMES SIN PHI B1
[810
[A=(VB*CPHI)-(WB*SPHI)
VB
RSLD
YTEM
(VB TO B9R
[TIMES SIN PHI 81
CYTEM = A 810
CVB*SPHI B10
EWB TO B9R
[TIMES COS PHI B1
WB
RCLD
[B = (VB*SPHI)+(WB*CPHI)
[B TO B10
ECLD
ZTEM
[B TO B1OR
[TIMES COS THETA 81
[zEM = B 810
UB
ESLD
[UB TO BiOR
[TIMES SIN THETA B1
(ADD ZTEM*STHETA B11
2
145
ARBR'F
MDAR'H
MPYU
BRMD
ARBR'F
MDAR'H
MPYU
NOOP
BRAE'F
ARBR'F'B
YAWTR:
BRAR'H'F
MPYU
BRMD
ARBR'F
MDAR'H'N
MPYU
NOOP
BRAE'F
ARBR'F
MDAR'H
MPYU
BRMD
ARBR'F
MDAR'H
MPYU
NOOP
BRAE'F
ARMD
JUMPI
ZTEM
ESLD
VZ
[C = (UB*STHETA)+ZTEM*STHETA
[ZTEM TO B1OR
[TIMES SIN THETA
[VZ = C 89
uB
ECLD
CUB TO BIOR
[TIMES C-5 THETA 81
(ADD STHETA*ZTEM
ED = UB*CTHETA + ZTEM*CTHETA
YCLD
XTEM
ID TO B1OR
(TIMES COS PSI B1
[XTEM = D B10
YTEM
YSLD
[YTEM TO B1OR
[TIMES SIN PSI 81
XTEM
YSLD
VX
[ADD D*CPSI
CE= CPSI*ZTEM + SPSI*YTEM
EXTEM TO B1OR
[TIMES SIN PSI B1
[VX = E 811
YTEM
YCLD
[YTEM TO B1OR
[TIMES COS PSI 81
VY
DIRCS
[F = XTEM*SPSI
(VY = F 811
+ YTEM*CPSI
[FOLLOWING SUBROUTINE COMPUTES DYNAMIC FORCES FROM VELOCITY AND
[AIRCRAFT DIMENSIONS AS WELL AS TRANSLATIONAL AERODYNAMIC FORCES
TRNSL:
MDAR'H
MPYU
NOOP
ARBR'H'F
BRAR'F
MPYI
NOOP
ARMD
BRAR'F
MPYI
NOOP
ARMD
BRAR'F
MPYU
NOOP
ARLS
NOOP
ARAR'H'F
ARBR'F
RHO
VT
[FROM ATMOS TO B-SR
[FROM AERO TO 810
(BR
SCRD2
QSCSQ
IS B2R
[1/4 * S * C * C B19R
.25*V*S*C*C
821
B24R
SSPN2
[.25*S*B*B
QS8SQ
[TIMES V
VT
[FORM V SQUARED
(PROD 812 (NEVER G.T. B10)
(DUE TO VARIATION OF MAX
2
B26
[AIRSPEED & DENSITY WITH
[ALTITUDE SO SHIFT TO 810
146
MPYI
NOOP
ARMD
BRAR*F
MPYI
NOOP
ARMD
BRAR'F
MPYI
NOOP
ARMD
816R
SCORD
[1/2*S*C
QSC
[TIMES V SQRED
SSPAN
[1/2 * S * 8 B18R
QSB
[1/2 *S*B* VSQR B28
SAREA
[1/2 * S B1IR
QS
[1/2 * S * VSQR B21
826
[THRUST COMPUTATION: (MACH VARIATION HERE, ALTITUDE IN ATMOS)
[THRUST = IDLE + (MAX-IDLE)(DELTA THROTTLE NORMALIZED SQRED)
THR:
/S.
MACH 812
MDAR'H
MPYU
MDBR
BRAE'F
ANAR
ARRS
ARMD
ITHVM
MACH
ITHMO
(IDLE
ZERO
3
IDTHR
[ZERO IF NEGATIVE
MDAR'H
MPYU
MDBR
ARPS
BRAE'F
MDAE'N
ARBR'F
MTHVM
MACH
MTHMO
[MAX VS.
MDAR'H
MPYU
BRMD
ARAR'H'F
MPYU
MDBR
BRAE'F
ARRS
ARMD
DTHRO
DTHRO
MXTHR
CIDLE(M=O) B12
[STORE IDLE B15
[MAX(M=0)
MACH 813
815
IDTHR
[NORMALIZED THROTTLE
[SQURRED 80
MXTHR
IDTHR
5
THRST
[THRUST ONE ENGINE B15
[SHIFT TO 820
[USE AS 822 (FOUR ENGINES)
147
(FOLLOWING VARIATION WITH MACH IS APPLIED TO C SUB L-ALPHA
[CLALP = 4,584 - 2,22 MACH + 5.378 MACH SQRED (IN RADIANS)
[ALPHA HERE IS FOR X BODY AXIS PLUS 1.9 DEG. INCIDENCE ANGLE
[ALSO FOR DFLAP GT. 6 DEG, ADD INCREMENT OF 1.081 / RADIAN
LCORR:
LFT:
NOFLP:
MDAR'H
MPYU
NOOP
ARAR'H'F
MPYI
NOOP
ARBR'F
MDAR'N'F
MPYU
NOOP
BRAE'F
MDAE
ARMD
MACH
MACH
MDAR
MDAE'H'N'F
JPAN
ARBR'H'F
MDAR'H'F
MDAE
ARMD
BRAR'F
MPY I
NOOP
ANAR
ARMD
MDAR
MDAE'H'F
ARBR'F
MDAE'H'N'F
JPAN
ARLS
ARAR'H'N'F
BRAS'H'F
JUMP
BRAR'H'F
MPYU
MDBR
BRAE'F
ARBR'F
MDAR 'F
MPYL
NOOP
ARRS
BRAE'F
ARBR'F
ARAR'H'F
MPYU
BRMD
DFLAP
DFLP6
NOFLP
25430
(5,387 83R
10703
MACH
(2. 22 B3R
CLO
CLALP
(4.584 83
[LIFT SLOPE VS. ALPHA 83
4246
CLALP
CLALP
CLFLA
ZERO
CLFL.P
ALPHA
2076
23774
,5
,2
[IF FLAPS G.T, 6 DEG
[THEN ADD INCREMENT
[OF 1.081 TO CLALP B3
[AND (FLAPS - 6) 80
[TIMES C SUB L-FLAPS B2R
POS,
[ANSWER SHOULD BE
[UNLESS JUMP FROM ABOVE
[THEN ZERO CLFLP 82
[ADD 1.9 DEG INCIDENCE
[IN RADIANS B-1
[SUBTRACT 17.9 DEG. STALL
[IF STALLED DECREASE
[ALPHA BY AMOUNT ABOVE
[CRITICAL THUS DECREASING
[CLIFT LINEARLY
CLALP
CLFLP
[FROM ABOVE B3
[FLAP CONTRIBUTION 82
CLELE
DELEV
[C SUB L-DELTA E B-1R
[DELTA ELEVATOR BOR
3
QS
CLI FT
[DYNAMIC FORCE 821
[TOTAL C SUB L 82
148
[LIFT TO B21
2
ARLS
LIFT
ARMD
(FOLLOWING CORRECTIONS ARE APPLIED FOR DRAG VARIATION WITH MACH
MACH L.T, .7
.012
CDMIN=
CKDRAG= .0524
.01233+.0033(M-.8) LT. .8
=
.0524
[
L.T. .845
=
.014+.0371(M-,8)
= .063+.2356(M-.8)
[
.014+.1455(M-.845) G,T. .845
=
= .063 +.8333(M-,845)
[
DCORR:
"DAR
MDAE'H'N'F
MGT84
MLT84:
MLT80:
MLT70:
JPAN
MbAE'H'N'F
JPAN
MpAE'H'N'F
JPAN
ARAR'H'F
ARBR'F
MPY I
NOOP
ARLS
MDAE'H'F
ARMD
BRAR'F
MPY I
NOOP
ARRS
MDAE'H'F
ARBR'F
JUMP
ARAR'H'F
ARBR'F
MPY I
NOOP
MDAE'H'F
ARMD'B
BRAR'F
MPYI
NOOP
MDAE'H'F
ARRS
ARBR'F
JUMP
ARAR'H'F
MPY I
MDBR'LJ
MDAE'H'F
ARRS
BRMD
ARBR'F
JUMP
MDAR'H'F
ARMD
MDBR'H'F
MACH
26314
MLT70
3146
MLT80
1341
MLT84
(.7
MACH 80
[.1 MACH B0
(.045 MACH 80
32524
[.8333 B0
3
20101
KDRAG
(.063 B-3
[USED LATER B-3
22477
[,1455 B-2
3
162
E.014 B1
[CDMIN B1
DRG
36120
(.2356 B-2
10015
KDRAG
(.063
22773
(.0327 B-4
7162
5
[.014 B-4
(HOLD CDMIN IN BR
DRG
6604
15324 1H
31200
7
KDRAG
DRG
15324
KDR AG
142
(.0033 B-6
(.0524 B-3
(.01233 8-6
(.0524
(.012
B-3
B1
149
DRG:
NOFL:
SDFOR:
PDAR'H
MPYU
NOOP
ARAR'H'F
MPYU
NOOP
BRAE'F
ARBR'F
MDAR'F
MPYL
NOOP
BRAE'F
ARBR'H'F
MDAR
MDAE'H'N'F
JPAN
ARAR'H'F
MPYI
NOOP
BRAE'H'F
ARBR'H'F
MDAR
ANAR
BRAS'F
MPYU
NOOP
ARLS
NOOP
ARBR'F
MDAR'F
MPYU
BRMD
ARBR'F
MDAR'F
MPYL
NOOP
BRAE'F
ARAR'H'F
MPYU
NOOP
ARLS
NOOP
ARMD
JUMP 'I
CLIFT
CLIFT
[FORM C SUB L SQRD 84
KDRAG
[CURVE COEFFICIENT 8-3
[ADD MINIMUM DRAG COEF.
CDSPL
DSPOL
[SPOILER COEF. BIR
DFLAP
DFLP6
NOFL
[ADD EXTRA DRAG FOR FLAPS
[OVER 6 DEGREES
CDFLP
[DELTA CDMIN DUE FLAPS 81R
GFLG
CDGER
[SUM TO B1R
(-0 IF DOWN +0 IF UP
(C SUB D-GEAR BiR
[ADD R.H. BiR
QS
5
[DRAG AS B22
[DRAG TO 617
CYBET
BETA
DRAG
(C SUB Y-BETA BOR
CYRUD
DRUDD
(C SUB Y-RUDDER B-IR
4
[SIDE FORCE TO B16
YAERO
TRNSL
[SIDE FORCE FOR WTOB
[DRAG FOR WTOB B17
150
[THE FOLLOWING SUBROUTINE COMPUTES THE AIRCRAFT MOMENTS FROM
[AERODYNAMIC FORCES
ROTAT:
RLL:
PTCH:
MDAR'H
MPYI
NOOP
ARRS
ARBR'F
MDAR'F
MPYL
NOOP
ARRS
BRAE'F
ARBR'F
MDAR'H
MPYL
NOOP
BRAE'F
ARAR'H'F
MPYU
NOOP
ARBR'F
MDAR'H
MPYI
NOOP
ARAR'H'F
MPYU
NOOP
ARRS
BRAE'F
DIVI
MDBR 'H
ARLS
NOOP
ARMD'H
BRAR'F
MPYU
MDBR
BRAE'F
ARBR'F
MDAR'F
MPYL
NOOP
BRAE'F
ARBR'F
MDAR
MDAE'H'N'F
JPAN
ARAR'H'F
MPYI
NOOP
BRAE'F
BETA
CBETA
[SIDE SLIP ANGLE TO B-1R
[ROLL COEF. DUE TO BETA B-2R
1
CRUDDDRUDD
(COEF. DUE TO RUDDER B-5R
[DELTA RUDDER FROM YCI'1 BOR
3
CAILE
DAILE
(COEF. DUE TO AILERONS TO B-2R
BOR
[DELTA AILERON
[FROM TRNSL B28
[PROD B26
PRATE
CPRT
[ROLL RATE TO B0
(COEF DEFINED B-1R
QSBSQ
[PROD TO B-IR
[FROM TRNSL 826
1
Ixx
CMALP
2
LMOM
ALPHA
CMO
CMELE
DELEV
DFLAP
DFL14
NFLP
CMFLP
[TOTAL ROLL MOMENT 826
(DIVIDED BY INERTIA B22R
[STORE AS B2 FOR EQMM
(C SUB M-ALPHA TO BiR
[ANGLE OF ATTACK B-IR
(COEF. DUE TO ELEY. BOR
[DELTA ELEVATOR BOR
[IF FLAPS G.T. 14 DEG
[THE FLAPS -14
[TIMES C SUB M-FLAP BOR
151
ARBR'F
NFLP:
YAW:
BRAR'M'F
MPYU
NOOP
AR9R'F
MDAR'F
MPYU
NOOP
ARAR'F'H
MPYU
NOOP
BRAE'F
DIVI
MDBR
ARLS
NOOP
ARMD'H
BRAR'H'F
MPYI
NOOP
ARRS
ARBR'F
MDAR'F
MPYL
NOOP
BRAE'F
ARAR 'H'F
MPYU
NOOP
ARBR'F
MDAR'H
MPYI
NOOP
ARAR'H'F
MPYU
NOOP
ARRS
BRAE'F
DIVI
NOOP
ARLS
NOOP
ARMD'H
JUMP 'I
QSc
[DYNAMIC FORCE B26
CMQRT
QRATE
[C SUB M-Q B5R
[80
QSCSQ
(821
[PRODUCT B26
[SUM AS B26
[INERTIA B23R
IYY
BETA
2
MMOM
CNBET
[STORE AS B1 FOR EQMM
[SIDESLIP ANGLE TO B-1R
[YAW COEF. DUE TO BETA B-3R
I
CNRUD
DRUDD
[YAW COEF. DUE RUDDER B-3R
[DELTA RUDDER BOR
QSB
[SUM TO B-3R
[DYNAMIC FORCE B28
RRATE
CNRRT
[YAW RATE TO B-iR
(COEF. DUE TO YAW RATE B-2R
QSBSQ
[DYNAMIC FORCE P26
2
IZZ
[SUM AS B25
[YAW INERTIA B23R
2
NMOM
ROTAT
[FOR EQMM 60
152
[FOLLOWING SUBROUTINES COMPUTES ATMOSPHERIC VARIABLES.
[COMPUTATION PROCEEDS ON THE ASSUMPTION THAT QUANTITIES VARY
[SLOWLY WITH ALTITUDE.
ATMOS:
[COUNT 15X'S /SEC
CLK2
MDAR'X
15
MDAS'N'F
[IF FIFTEENTH
ACONT
JPAN
CLK2
ARMD
[INCREMENT CLOCK SECS
TTIME
MDAR'X
$CLCKF
MDAR
ACONT
JPAN
[FORM CLOCK DISPLAY
STMDSP
JPSR
ATMOS
JUMP I
[CREATE JUMP
ATCNT
ACONr:
MDAR'X
[NEXT ROUTINE
MDAE'L
ATLST-1
JUMP'I
[JUMP THERE
ARIR'F
[IF ALTITUDE L.T. 5000
$R
MDAR
-5000.!K
MDAE'L
[DO MKLTS
$MKLTS
JSAN
ATMOS
JUMP'I
ATLST:
ATMO1JATM02ATM03)ATMO4;ATM05
[RHO/RHOO = 1 - 1.835(R/65536) + 1 (R/2**16)**2
[DIVIDE BY 65536
RB16
ATMOl:
MDAR'H
[I.E. NOW NORMALIZED 80
RB16
MPYU
[SQUARED IS 80
RB16
MDBR'H'N
ARRS
1
[STORE SQUARE AS 81
RSQR
ARMD
[RECALL R816 AS B16R
BRAR'F
[1.835 AS 81
35270
MPYI
[+1 TO BR AS B0
FS
MDBR'H
RSQR
MDAE
[SHIFT SUM TO B0
1
ARLS
[ADD +1
BRAE'F
ARAR'H'F
[RHO ZERO B-SR
RHO0
MPYI
NOOP
[STORE RHO B-8R
RHO
ARMD
ATMOS
JUMP'I
[FOLLOWING SUBROUTINE IS USED HERE AND IN 4D COMPUTATIONS
BELOW 36.089 FT
[A/AO = 1 - (3,6825*10**-6)(ALTITUDE IN FEET)
ABOVE 36,089
[A/AO = .867
[COMP, SPEED OF SOUND
,
SOUND:
[HOLD ALTITUDE
ARBR'F
[SUBTRACT 36,089 FT B16
21476
MDAE'H'N'F
[SPEED OF SOUND ABOVE
. 3
JPAN
[36,089 IS CONSTANT
17074
MDAR'H'F
[USE 967.6 FT/SEC B11
SOUND
JUMP'I
[LAPSE RATE FOR A/AO IS
BRAR'N'H'F
P ER FT AS B-16
[3,6826*10**-6
7562
MPYI
[PRODUCT IS B0
FS
MDBR'H
[ADD +1 AS 80
BRAE'F
ARAR'H'F
[TIMES 1116.4 FT/SEC B11
21343
MPYI
153
NOOP
JUMP'!
SOUND
ATM02:
MDAR
RB16
[ALTITUDE B16
JPSR
SOUND
ARMD
SPDSN
[LOCAL SPEED OF SOUND 811
JUMP'I
ATMOS
[FOLLOWING COMPUTES A LINEARIZED CONVERSION FACTOR FOR
[CONVERTING
MACH TO INDICATED AIRSPEED
[WHERE KIAS = M21iAS * MACH
(KIAS IN KNOTS 810)
[AND M2IAS = 656 - c,0091)(ALTITUDE IN FEET)
[ALSO THE ANGULAR DIFFERENCE BETWEEN 7 MACH AND 300 KNOTS
[FOR ROTATION OF THE MACH INDICATOR
ATM03:
MDAR'H'N
RB16
[ALTITUDE AS 816
MPYI
22506
[TIMES .0086 AS B-6R
NOOP
MDAE'H'F
24400
ARMD
M2IAS
[CONVERSION IN KNOTS B10
ARAR'H'F
MPYI
1205
.9 DEGREES PER KNOT
NOOP
[.7 MACH = .63
AS 84
MDAE'N'H'F
416
[.9 * 300 KNOTS AS B14
ARMD'H
$MHANG
[ANGLE FOR MACH SCALE
JUMP'I
ATMOS
ATM04:
JPSR
$MACHC
[SET UP MACH SCALE
JUMP'I
ATMOS
(IN. "FNST2"
[FOLLOWING CORRECTIONS ARE APPLIED TO THRUST/ ENGINE VS, ALTITUDE
[MAX CONTINUOUS (M=O) =13800 - .28125 (ALT IN FT)
[MAX THRUST DEC. WITH MACH = -7800 +.3117(ALT IN FT)
ALT L.T. 15000
[
-3125 +.185(ALT - 15000) ALT G.T. 15000
[IDLE THRUST(M=0)
= 1000 LBS. ALL ALTITUDES
[IDLE THRUST DEC. WITH MACH = -2000
ALT L.T 15000
[
= -2000+.07(H-15000)
G.T.15000
ATMOS:
MDAR
RB16
MDAE'H'N'F
7246
[15000 FT B16
JPAN
BLW15
ARBR'F
ARAR'H'F
MPYI
27534
(.185 B-2R
NOOP
MDAE'H'F
71712
[-3125 814
ARMD'B
MTHVM
[MAX THRUST VS MACH B15
BRAR'H'F
MPYI
21727
(.07 B-3R
NOOP
MDAE'H'F
70137
(-2000 B13
ARMD'8
ITHVM
(IDLE THRUST VS MACH
612
JUMP
MTCOM
BLW15:
MDAR'B
R816
ARAR'H'F
(.3117 B-IR
MPYI
23745
MDBR'L;
60277!H
(-2000 812
MDAE'H'F
60607
(-7800 814
BRMD
ITHVM
ARMD'B
MTHVM
154
MTCOM:
[-.28125 B-IR
MDAR'F
55777
MPYU
RB16
NOOP
MDAE'H'F
[13800 815
15364
ARMD
MTHMO
[MAX (M=0) 815
ARXO'F
ARMD
ATCNT
ATMOS
JUMP'I I
ATCNT:
0
RB 16:
0
RSQR:
0
[FOLLOWING SUBROUTINE INTEGRATES VEHICLE FRAME VELOCITIES TO
[OBTAIN EARTH FRAME POSITION. NOTE THE CHANGE OF COORDINATE AS
[DISPLAY +Y AXIS POINTS NORTH AND +X EAST WHILE THE
[OPPOSITE IS TRUE IN VEHICLE FRAME
[INTEGRATION RULE: X(N) = X(N-1) + H/2 (2 VX(N))
INTGV:
,
MDAR 'B
VX
[2X'S VEHICLE X VEL. B11
MDAE'B
WVX
[PLUS X WIND VELOCITY
ARAR'H'F
MPY I
DT15
[DELTA T/2 B-4R
NOOP
ARRS
16.
[SHIFT TO B23
MDBR'B
VY
ARMD
GVX
Q
MDAE
Q
ARMD
(EARTH Y POSITION 823
ARMD
$YP
[Y POSITION FOR "MMAP2"
BRAR'F
[2X'S Y VEHICLE VEL B11
MDAE'B
WVY
[Y WIND VELOCITY
ARAR'H'F
MPYI
DT15
NOOP
ARRS
16.
MDBR'N'B
VZ
ARMD
GVY
MDAE
P
ARMD
[EARTH X POSITION 823
P
[X POSITION FOR "MMAP2"
ARMD
DP1
BRAR'F'H
MPY I
NOOP
ARRS
MDBR
BRAE'F
ANAR
ARMD
ARLS
NOOP
ARMD
MDAR
MPYL
NOOP
[2X'S NEG VZ 89
DT15
18.
R
[ALTITUDE B23
ZERO
R
7
[PREVENT ALTITUDE FROM
(GOING NEGATIVE
R816
GVX
GVX
(STORE AS B16 ALSO
[CALCULATE GND SPEED
(FT PER UPDATE BSR
ARBR'F
MDAR
MPYL
NOOP
BRAE'F
JPSR
MPYI
NOOP
MDAR'H'A
ARRS
ARMD'H
JUMP'I I
FRINC:
FHINC:
RLIM:
QS: 0;
QSBSQ: 0;
RHO:
SPDSN:
MACH:
KIAS:
M2IAS:
THRST:
IDTHR:0;
MTHVM:
MTHMO:
ITHVM:
ITHM0:
WVEL: 0;
GSPD: 0;
VX: 0;
P:0;
ALPHA: 0;
BETA: 0;
LIFT:0;
XTEM: 0;
UBN: 0;
GECRS: 0;
PRANW : 0;
DTEM : 0
RSECQ: a;
UB: 1500 1H;
UBSQ: 0;
VT:12240!H;
PRATE: 0;
PDOT: 0;
LMOM: 0 ;
UDOT:0;
XBM: 0;
DELEV:0;
DSPOL:
DFLAP: 0
FRATE':
DTHRO:
100, !K
3038. K
50000.! K
QSB: 0;
QSCSQ: 0
23360 ! H
21227! H
0
0
23610! H
5442000
MXTHR: 0
60607!H
15364!H
60277!H
7640!H
GVX:0
Q:0)
SINA:0;
SINB:0;
DRAG:0;
YTEM:0.
VBN: 0
GECRC: 0
PQ:0;
RCECQ:0;
VB: 0;
VBSQ:0;
QRATE:0;
QDOT: 0;
MMOM:0;
VDOT: 0;
YBM:0;
DAILE:0;
0
16!H
0
155
GVY
GVY
[DELTA DIST SQRED 816
$SQRT
10706
[DELTA T X'S KTS/FT B5R
FS
GSPD
INTGV
QSC: 0
WVt: 0
GV : 0
VZ: 0
R:500. !K
COSA: 0
COSB:200001H
YAERO:0
ZTEM: 0
RQ:0
RCECRI:0
WB:0
WBSQ: 0
VSQR:O0
RRATE:0
RDOT:0
NMOM:0
WDOT:O0
ZBM:0
DRUDD:O0
[DROP BIT 29
[KNOTS B14R
[ALTITUDE INCREMENT
[HORIZ INCREMENT
[ALTITUDE LIMIT
[DYNAMIC FORCE TERMS
[FROM TRNSL
[ATMOSPHERIC DENSITY B-8R
[SPEED OF SOUND 811
[MACH NUMBER
[INDICATED AIRSPEED B10
[CONVERSION FACTOR BIG
[THRUST
[IDLE AND MAX
[MAX VS. MACH 813
[MAX CONTINUOUS(M=0) 815
[IDLE VS, MACH B12
[IDLE(M=0) 812
[WIND AND COMPONENTS
[GROUNDSPEED AND COMPS
[VEHICLE VELOCITY
[VEHICLE POSITION
[ANGLE OF ATTACK
[SIDESLIP ANGLE
[WIND AXIS FORCES
[USED IN DIRCS
[TEMP STORAGE IN FORCE
[RESOLVE G IN FORCE
[TEMP STORAGE IN EQMM
[TEMP STORAGE IN WTOB
[TEMP STORAGE IN EULER
[BODY AXIS VELOCITIES
[SQUARE IN AERO
[TOTAL VELOCITY
[ANGULAR RATES
[ANGULAR ACCELERATIONS
[MOMENTS DIVIDED BY MASS
[BODY AXIS ACCELERATIONS
[AERO FORCES BY MASS
[CONTROL DEFLECTIONS BOR
[SPOILER DEFLECTIONS BOR
[COMPUTED FLAP POSITION 80
[FLAP RATE 50 DEG, IN 30 SEC
[COMMANDED THROTTLE POSITION
156
CLALP:
CLOt
CLFLP:
KDRAG:
CDGER:
CAILE:
CM0 :
CMALP:
SSIX0 :0;
SSIX3 :0;
NZERO:
GFLG:
SCALE
MSK :
MK1:
ZERO:
SEVEN:
READY:
FNSWS:
CLK2:
TTIME:
NFS:
FS:
NEGAT:
NEGB:
ONE62=10000
TERMINATE
22254! H
22254! H
0
15324! H
126
137021H
1422 !H
60560 !H
SSIX1 :0;
SSIX4 :0
-0
0
2
77777
77776
SSIX2: 0
[SLOPE OF LIFT COEF, B3
[MIN SLOPE OF LIFT COEF. 63
[C SUB L DUE TO FLAPS 82
[DRAG CURVE COEF. B-3
[DRAG COEF. DUE TO GEAR BiR
[ROLL COEF. DUE AILERONS B-2
[MINIMUM PITCH COEF. B0
[PITCH COEF. DUE TO ALPHA 61
[SHARED SOURCE SIX
[REGISTER STORAGE
[GEAR FLAP -O=DOWN
[MOVING MAP SCALE
0
7
0
0
0
0
40000
37777
ARAR'N'F
BRBR'N'F
[MASK
[FREEZE FLAG
[15 COUNTS/SEC
[PROGRAM CLOCK TIME
[NEG FULL SCALE
[POS FULL SCALE
[INSTRUCTION TO CHANGE
[SIGN OF AR AND BR
157
APPENDIX B
THE FOUR-DIMENSIONAL NAVIGATION PROGRAM
A portion of the assembly language program which solves
the time-controlled navigation equations is included here.
The logic of the various subroutines is shown in the
ciated comments.
asso-
The omitted portions of the program are
uniquely associated with the Adage
computer's graphic display
or the moving map used in this simulation.
158
TITLE
FOURD
EXPUNGE
[THIS PROGRAM DISPLAYS ASSIGNED TIME, ALTITUDE, AND SPEED
[FOR FOUR DIMENSIONAL WAYPOINTS. THE DISPLAY AND MOVEMENT
[OF WAYPOINT DATA HAS BEEN ADAPTED FROM ANDERSON'S TRFFL
[ROUTINES FOR TRAFFIC MOVEMENT. C.J. CORLEY 9/74
[IT ALSO CONTAINS THE COMPLETE MIN TIME - MAX TIME
[CONTROLLER COMPUTATION FOR MEETING ASSIGNED TIMES
[AND FOLLOWING A FOUR DIMENSIONAL ROUTE, C.J.C. 11/74
ENTRY
ENTRY
ENTRY
ENTRY
ENTRY
ENTRY
ENTRY
ENTRY
ENTRY
WDRAW,WMOVE,SIDL,FORD1.,MXDRW,MNDRW
TDP,TDA,TAP,TDS,TSP,TDT,TTP,TD2,TX
TY,TTDRW,STDRW,TIME1,TIME2,SDISF
S60WP,S62WP,S63WPSTRBF,CLCKF, TMDSP
SPSET.,VERGR,SBUGD,DBUGD,CMSPCSVLST
WPSELSELST.,WPIDO.STG3L,MXTIMMNTIM
ACCEL,DECEL,PROFL,MXASPMNASPPTAFL
STAGE,WPX,MXTA,MNTA,FINZFINAS
FINTM,SUM
[4D NAV CALLED BY ACSM2
FORDI:
MDAR'L
JPSR'I
MDAS'X
ARIR'F
JUMPI
FDPTR:
FDLST:
16
PROFL
MXASP
MNASP
CMSPC
PROFL
MXASP
MNASP
CMSPC
MXDSP
MNDSP
PROFL
MXASP
MNASP
CMSPC
FDESR
FDLST-1
FDPTR
[EACH CALL DO NEXT IN FDLST
FORDI
[VERTICAL GRADIENT AND SEGMENT
[TIME TO DESCEND AT MAX SPEED
[TIME TO DESCEND AT MIN SPEED
[COMMAND SPEED BUG
[CREATE EARLIEST ETA DISPLAY LIST
[CREATE LATEST ETA DISPLAY LIST
[INITIALIZE
SUBROUTINE LIST
FDESR:
MDAR
JPAN
MDBR'F
MDAR'H
MPYI
BPMD
ARBR'F
MDAR
MDAE'H'F
SELST
FDES1
16
SPSET
3462
FDPTR
[SELECT NEG
[STORE POSITIVE
[COME HERE ON NEXT PASS
[IN STORE MOVE SPEED
[BUG WITH COCKPIT KNOB
$R816
63625
[IF ALTITUDE 816
[G.T. 25000
159
FDES1:
JPAN
MDAR'H
BRAE'F
ARBR'F
BRMD'H
JPSR
ARMD'O
ARMD'O
JUMP 'I
MDAR'F
ARMD
JUMP 'I
. 4
$MHANG
[TO SET CONSTANT MACH
SBUGA
SBUGC
$SAVIF
$SAV3F
FDESR
0
FDPTR
FDESR
[NEG FOR NEXT SELECT CYCLE
[IN SELECT BEGIN S/R LIST
[WITH PROFL
[FOLLOWING CODING FORMS TWO ROUTINES MXASP AND MNASP WHICH COMPUTE
[TIMES OF ARRIVAL BASED ON MAX SPEED AND MIN SPEED
AA=MXASO
BB=ASO
CC=ACCEL
DD=DECEL
EE=MXAS3
FF=FINAS
GG=ASO
HH=FINAS
IREPEAT NNCMXMN)
NN\ASP:
NN\L1:
MDAR'F
ARMD'N
ARMD'O
6
ITERC
ITERF
[COUNTER TO LIMIT
(NO, OF ITERATIONS
[ITERATION FLAG
MDAR
ARMD
MDAR
MDAE'N
ARBR'F
ARRS
ANAR
DIVU
NOOP
ARMD
BRAR'F
ARRS
MDAE
ARAR'H'F
MPYL
MDBR
ARMD
BRAE'N'F
JPAN
ARRS
MDBR
MPYU'N
BRMD
STG3
DCDST
AA
BB
[INITIALIZE ASP CHANGE
[DISTANCE FROM PROFL
6
ZERO
CC
[TO B16
[PREVENT GOING NEG
[RATE OF CHANGE B3
NN\TM0
[TIME REQ. IN SECS B13R
[COMPUTE AVE ASP
[DURING CHANGE (FT/SEC) 610
1
BB
NNNTMO
STG1
NNNDO
NN\L2
10.
ZERO
TANSL
NN\TM1
[AIRSPEED DIFFERENCE 610
[TIMES TIME 813R
(DIST TO CHANGE B23
[MINUS DIST AT INIT ALT
(NEG IF STG 1 GREATER
(USE AS B1SR
[DIST TO ALT BY TAN B-2
[ZERO TIME IN LEV FLT
160
NN\L2:
MDAE
ARMD
JUMP
INITZ
NN\SLZ
NN\L3
[SUB FROM INIT ALT 816
[SLOPE ENTRY ALT. 816
DIVU
NN\ASO
INITZ
NN\TM1
NN\SLZ
NN\AVR
NNNSL Z
FINZ
(DIST AT NEW ASP B10
COTSL
[COT SLOPE B7
MDBR
NN\L3:
NNAL4:
ARMD'N
BRMD
JPSR
MDAR
MDAE'N
ARAR'H'F
MPYU
NOOP
ARBR'F
JPAN
JUMP
MDAE
ARMD
BRAR'F
ANAR
DIVU
MDBR
ARMD
MDAR
BRAE'N'F
ARBR'F
ARRS
ANAR
DIVU
NOOP
ARMD
BRAR'F
ARRS
MDAE
ARAR'H'N'F
MPYL
MDBR
ARMD'N
BRAE'F
ANAE
JPAN
ARMD'O
JUMP
MDAR'H'N'X
JPAN
MDAR
ARMD
ARXO'F
ARMD
MDAR
ARMD
, 2
NN\L4
STG3
DCDST
ZERO
NN\AVE
FF
NN\TM2
EE
[LV, FLT TIME AT NEW B13R
[SLOPE ENTRY 816
[AVE SLOPE AIRSPEED
[SLOPE ENTRY TO B16R
[MINUS FINAL AS B16R
[SLOPE HORIZONTAL DIST 823
[IF NEGATIVE
[DECREASE DECELERATION
[DIST BY THIS AMOUNT
[DIST OR ZERO 823
[AVE ASP FOR SLOPE 810
[SLOPE TIME 813R
[AIRSPEED DIFF. 810
6
ZERO
DD
[TO 816
NNNTM3
[FINAL ACC/DEC TIME B13R
[DIFF. FAST - SLOW
[DIVIDE BY 2
[PLUS SLOW
[GIVES AVE ASP TO B1OR
1
FF
NN\TM3
DCDST
NN\D3
TOLER
, 3
ITERF
NN\L6
ITERC
NN\LS
FINAS
LOBND
ITERF
NN\AS3
HIBND
[RATE OF CHANGE 83
[CHANGE DIST B23
[IF DISTANCE LEFT
[PLUS TOLERANCE
[L.T, CHANGE DIST ITERATE
[ELSE SKIP
[COUNT ITERATIONS
[NOT FOUND BY ITERATION
[SET UP ITERATION BOUNDS
[CHANGE FLAG
161
NN\L5:
NN'L6:
NN\L7:
MDAE'N
ARRS
ARBR'N'F
MDAE'N
ARMD'N
MDAR
BRAE'F
ARMD
MDAR
BRAE'F
ARMD
JUMP
LOBND
1
[JUMP HERE WITH HIBND
(IN AR. DIVIDE BY 2
NN\ASO
NN\ASO
NN\AS2
[CHANGE EACH ASP
[BY (HIBND-LOBND)/2
DIVU
MDBR
ARMD
BRAR'F
JPAN
MDAR'H'N'X
JPAN
MDAR
ARMD
MDAR
ARMD
JUMP
MDAR
MDAS
MDAS
MDAS
MDAS
MDAR'A
ARRS
ARMD
JUMP 'I
NN\AS3
ITERF
NN\TM4
NN\AS2
NN'AS3
NN\AS3
NN\L1
NN\L7
ITERC
NN\L7
HIBND
LOBND
NN\AS3
HIBND
NN\L5
NN\TMO
NN\TM1
NN\TM2
NN\TM3
NN\TM4
MSK
1
NN\TIM
NN\ASP
[START OVER WITH NEW
[TIME BEFORE CHANGE B1:sR
[IS ITERATION IN PROGRESS?
[NO, EXIT
EYES CHANGE BOUNDS
(LAST PASS
[SUM ALL TIMES
[DROP LEFT HALF
[SHIFT TO B-29
[STORE
[JUMP TO HERE WHEN ITERATION HAS PRECLUDED POSSIBILITY
[OF TWO AIRSPEED CHANGES IN REMAINING DISTANCE
NN\LS:
MDAR
MDAE'N
ARBR'F
ARRS
JPAN
DIVU
NOOP
ARMD
BRAR'F
ARRS
MDAE
ARAR'H'N 'F
MPYL
MDBR
BRAE'F
JPAN
ASO
FINAS
(IS CURRENT AIRSPEED
[GREATER THAN- FINAL?
6
NN\L9
DECEL
[SHIFT TO B16
[FINAL G.T. CURRENT JUMP
[ELSE DECEL TIME
NN\TM3
[STORE B13R
1
FINAS
[COMPUTE AVE ASP
(DURING DECEL
NN\TM3
STG3
[COMPUTE DIST TO DECEL
[REMAINING DIST TO W.P.
[SUM B23
[NOT ENOUGH DIST JUMP
NN\L1O
ARBR'F
DIVU
NOOP
ARMD
MDAR
ARMD
MDAR'N
BRAE'F
JPAN
JUMP
NN\L9
NN\LIO:
NN\L11
NN\L12:
DIVU'N
NOOP
ARMD
BRAR'N'F
ARRS
MDAE
ARAR'H'N
MPYL
MDBR
BRAE'F
JPAN
ARBR'F
DIVU
NOOP
ARMD
MDAR
ARMD
MDAR'N
BRAE'F
JPAN
JUMP
ARXO'F
ARMD
MDAR
ARMD
ARMD'O
MDAR
MDAS
MDAR'A
ARRS
ARMD
JUMP ' I
AA=ASO
BB=MNASO
CC=DECEL
DD=ACCEL
EE=FINAS
FF=MNAS3
GG=FINAS
HH=ASO
END I
162
GG
NN\TM4
GG
NN\ASO
RE1ICT
[REMAINING DIST AT FAST
(OR SLOW GIVES TIME B13R
[LIMIT EXTREME TO
[FAST OR SLOW
[IS DIST REMAINING
[L.T. REACTION DIST
NN\L11
NN\L12
ACCEL
(ACCEL TIME
NN\TM3
ASO
NN\TM3
STG3
[COMPUTE DIST TO ACCEL
NN\L 10
[NOT ENOUGH DIST JUMP
HH
[REMAINING DIST AT FAST
NN\TM4
HH
NN\ASO
REACT
[LIMIT EXTREME TO FAST
[OR SLOW
L.T.
(IS DIST REMAINING
[REACTION DIST
NN\L11
NN\L12
[NOT ENOUGHT TIME
NN\TM4
FINAS
NN\ASO
NN\ASF
NN\TM3
NN\NTM4
MSK
[OR INSIDE REACTION
[DISTANCE
[SET FLAG FOR CMSPC
[SUM TIMES B13R
[TO 814R
NNNTIM
NN\ASP
163
MNAVR:
MDAR
MDAE'N
ARRS
MDAE
ARMD
JUMP 'I
MNASO
(SIMPLE AVE AIRSPEED
ZDURING DESCENT
MNAS3
MNAS3
MNAVE
MNAVR
[RUDIMENTARY LINEARIZED AVERAGE AIRSPEED DURING DESCENT
MXAVR:
MDAR
MDAE'L
50000. !K!K
JPAN
MDAR
MDAE'N
JPAN
ARMD
BRAE'F
ARMD
MDAR
MDAE'N
ARRS
MDAE
ARAR'H'F
MPYU
BRMD
ARBR'F
MDAR
MDAE'N
ARRS
MDAE
ARAR'H'F
MPYU
NOOP
BRAE'F
DIVU
NOOP
ARMD'H
MXAV1:
MDAR
MDAE'N
ARRS
MDAE
ARMD
JUMP 'I
MXSLZ
MXAV1
.-2
FINZ
MXAVI
DF2
DFT
MXAS2
MXAS3
1
MXAS3
DF2
DF1
[ENTRY ALTITUDE 616
[SUBTRACT
[25000 FT B16
[BELOW 25000 SIMPLE AVE
[OR IF FINAL ALT 616
[ABOVE 25000, SIMPLE AVE
[ELSE 25000-FINZ=DF2
[MXSLZ-FINZ =DFT (TOTAL)
[AVE BELOW 25K TO BOR
[TIMES DF2 816
[MXSLZ-25000 = DF1
[HOLD B26
MXASO
MXAS2
1
MXAS2
[AVE ABOVE 25K TO B1OR
DF1
DFT
[SUM B26
[TOTAL DIFF B16
MXAVE
[AVE AIRSPEED 610
MXASO
MXAS3
I
MXAS3
MXAVE
MXAVR
[COMPUTE SIMPLE AVE B10
164
[SET UP WAYPOINT AND ASSIGNED TIME FOR DISPLAY AND COMPUTATION
CENTER WITH SOURCE SIX REGISTER TWO IN AR
862WP:
,
ARMD
MDAR'H'A
ARBR'H'F
MDAE'H'N'F
JPAN
JUMP 'I
MDAR
JPAN'I
MDAR
MDAS'F
ARMD
ARMD
BRAR'F
MPYI
BRMD 'I
ARRS
MDAS'F
ARMD
MDBR'F
MDAR
ARBR'A'F
ARRS
BRMD
MDBR'F
ARBR'A'F
ARRS
BRMD
MDBR'F
ARBR'A'F
MDAR'F
MPYL
BRMD
ARBR'H'F
MDAR'F
MPYL
NOOP
ARRS
MDAS
ARBR'O'F
MDAR
BRXO'F
ARAR'H'O'F
JPLS
JUMP 'I
BRAR' F
MPYI*
BRMZ
BRAS'H'F
ARRS
ARMD'I 'X
WPTEM
MSK17
WPMUM
, 2
S62WP
SELST
S62WP
WPSEL
WPIDO
WPTR1
WPTR2
7
WPTR1
1
DLST
WPTR3
17
WPTEM
[NO OF WAYPOINTS
[INVALID WAYPOINT ID
[SELECT/STORE IN SELECT
[0,4,8,,,,
[1ST & 2ND POINTER
[TO TOP OF VALUE LIST
[1ST LABEL LIST LOCA
[CONTAINS ID NUMBER
[CONTAINS ASSOCIATED
[W.P. ID
4
ATA3
17
4
ATA2
17
6
ATA3
ATAl
(6 SECONDS 814R
[THIRD DIGIT B14R
(BR HOLDS SECONDS B13
10,
(10'S OF MINS, B14R
ATA2
WPATA
, 2
S62WP
60,
WPATA
I
WPTR1
(ADD UNIT MINUTES
(HOLD SECS L.H. B13
(MINS R.H. B14R
[RETURN IF SAME ATA
(MINS, B14R
(60 SECS B14R
[UPDATE ATA
(ADD SECS B28
(SHIFT SUM TO B29
(STORE IN VALUE LIST
TION
165
MDAR
MDAS'F
ARMD
MDAR'I
ARMD
MD&R
MDAR
JPSR
WPTR3
5
POINT
POINT
S621
TItXY
WPATA
TIMEC
JUMP'I
S62WP
5621:
[SET UP WAYPOINT ALTITUDE AND AIRSPEED FOR DISPLAY AND COMPUTATION
CENTER WITH SOURCE SIX REGISTER THREE
IN AR
S63WP:
ARMD
ARRS
MDBR
ARBR'A'H'F
MDAR'A
ARMD
ARMD
BRMD
BRMD
MDAR
JPAN 'I
MDAR
ARRS
MDBR
ARBR'A'H'F
MDAR ' A
ARMD
MDAR'O'K
ARMD
BRMD
MDBR'0'K
BRMD
MDAR
ARBR'H'F
MDAR'A
ARMD
MDAR'O'K
ARMD
MDBR'A
BRMD
MDBR'O'K
BRMD
MDAR
MDAS'F
ARMD
MDAS'F
ARMD
WPTEM
8.
MSK3
MSK3
ASP I
WPASP
ALTD1
WPALT
SELST
S631IP
WPTEM
4
MSK17
[LIMIT ALTITUDE TO 39,900 FT
[LIMIT AIRSPEED TO 399 KNOTS
[1ST AIRSPEED DIGIT
[IST ALTITUDE DIGIT
[SELECT/STORE IN SELECT
MSK17
ASP2
WPASP
WPASP
ALTD2
WPALT
WPALT
WPTEM
MSK 17
ASP3
WPASP
WPASP
MSK17
ALTD3
WPALT
WPALT
WPSEL
WPIDO
WIPTR2
2
WPTR1
[SKIP ID AND ATA
166
MOAR
BRXO'F
JPLS
MDAR
WDXO
JPLS
JUMP'I I
NWALT:
MDAR'F
MPYL
BRMD
ARBR'F
MDAR'F
MPYL
NOOP
BRAE'F
ARBR'F
MDAR'F
MPYL
NOOP
BRAE'F
ARLS
NOOP
ARMD'I
ARMD
MDAR
MDAS'F
ARMD
MDAR 'I
ARMD
MDAR
MDBR
JPSR
LDALT
(OLD ALTI.LABEL
NWALT
LDASP
WPASP
NWASP
S63WP
[NEW ALTITUDE
(OLD AIRSPEED LABEL
100.
ALTD3
LDALT
[NEW AIRSPEED
[STORE TEST ALT LABEL
1000.
ALTD2
10000,
ALTD'1
12,
WPTR1
WPR16
WPTR3
3
POINT
POINT
S631
LDALT
ALTXY
[STORE ALT IN FT B16
(STORE ALT 816
$LABRT
S631:
NWASP:
JUMP 'I
S63WP
MDBR
MDAR'F
MPYL
BRMD
ARBR'F
MDAR'F
MPYL
NOOP
BRAE'F
ARRS
MDAE
ARLS
MDBR
ARMD
BRAR'H'N'F
MPYI
NOOP
MDAE'H'F
WPASP
10.
ASP2
LDASP
[CHANGE TEST AIRSPEED LABEL
100.
ASPI
1
ASP3
19.
WPR16
WPTEM
21471
24340
[AIRSPEED IN KNOTS B29
[SHIFT TO B10
[ALT TO B16R
CIAS TO MACH CONVERSION
[SEE "ACSM2"
167
ARMD
MDAR
DIVU
NOOP
ARMD
BRAR'F
JPSR
ARAR'H'F
MPYL
NOOP
ARMD'B'I'X
MDAR
MDAS'F
ARMD
MDAR'I
ARMD
MDAR
MDBR
JPSR
WPTR1
WPTR3
4
POINT
POINT
S632
LDASP
SPDXY
$LABRT
JUMP 'I
S63WP
WPI2M
WPTEM
WPI2M
[IAS IN KNOTS B10
[CONVERSION 810
WPTEM
[MACH BOR
$SOUND
(SPD OF SOUND TO Bl1R
WPTEM
(STORE TAS FT/SEC
B10
S632:
POINT:
[READ DI SCRETE 4/D INPUTS FROM "ACSM2"
S60WP:
MDAR
ARBR 'H'F
ARRS
BRBR'B'F
MDAR'A
ARLS
ARMD
BRAR'K'F
ARMD
ANAR
JPAN
MDAR 'N
ARMD
JUMP 'I
SELEC:
ARMD'N
MDAR
MDAS'F
ARMD
MDAR' I
JPAN'I
ARAR'B'F
MDAS'F
ARMD
MDAR' I
ARMD
MDAR' I'X
ARMD
$SSIXO
(S6(15) 1ST IN BR
[S6(25) LAST IN AR
[S6(16) 1ST IN BR
MSK3
2
WPSEL
SELST
FLAG
SELEC
SELST
FLAG
S60 WP
FLAG
WUPSEL
UP IDo
SLPTR
SLPTR
S60 UP
VLST
POINT
POINT
WPX
POINT
WPY
[MULTIPLY BY 4
[0..4,8,...
(36(22) 1ST IN AR
[STORE = +GARGAGE,
[SELECT = -, 1ST PASS?
(YES., COMPUTE
[NO, THEN FLAG = NEG
[FOR STORINGPOS FOR
[NEXT SELECT
[FLAG POS 2ND PASS
[POINTER TO STORED VALUES
[SELECTED STORED WAYPOINT
[RETURN IF NONE STORED
[ELSE 2X'S WAYPOINT
[PLUS VLST
[GIVES POINTER TO
[WAYPOINT X.Y VALUES
168
MDAR'I'X
ARMD
MDAR'H'I'X
JPLS
MEAR'H
4RAR'H'F
ARMD
JPSR
BRMD
ARMD
MDAR' I'X
JPLS
MDAR
ARMD
MDAR
ARMD
MDAE'N
ARAR'H'F
MPYU
MDBR
ARMD
BRMD
ARMD'O
JUMP 'I
SLPTR
FINTM
SLPTR
, 2
$RB16
FINZ
MIMAS
FINMX
F INMN
SLPTR
, 2
$VT
FINAS
$RB16
INITZ
FIN Z
COTSL
$VT
SLOPE
CMDSP
$SAV2F
S60WP
[STORED ASSIGNED TIME
[STORED ALTITUDE
[ELSE CURRENT AS 816
R
(SET EXTREMES AT FINAt ALT
[STORED AIRSPEED
[ELSE CURRENT
(INITIAL ALTITUDE 816
[MINUS FINAL
[COT OF SLOPE B7
(SLOPE DIST IN FT 823
[SAVE INITIAL VALUES
(FOLLOWING S/R DOES ENTIRE VERTICAL SLOPE CONTROL AND SETS VALUES
(TO BE USED IN MXASP AND MNASP
PROFL:
.
ARXO'F
ARMD
STG1
[LEV FLT AT INITZ ZERO
SEGIF
[SEGMENT FLAGS
ARMD
ARMD
SEG2F
ARMD
SEG3F
[INITIALIZE STG3
MDAR
.STG3L
ARMD'N
STG3
[MAKE TRUE AIRSPEED LOCAL
$VT
MDAR
ARMD
ASO
[RESET EXTREMES AFTER ITERATION
MDAR'H'F
34124
MXAS2
(25000 FT
ARMD
MDAR'H'F
17021
ARMD
MNAS2
[FINAL ALTITUDE
MDAR
FINMX
MXAS3
ARMD
FINMN
MDAR
ARMD
MNAS3
[ESTABLISH EXTREMES
MDAR
$RB 16
[FOR THIS ALTITUDE
JPSR
MIMAS
BRMD
MXASO
ARMD
MNASO
[SELECTED WAYPOINT X VALUE
MDAR
WPX
PRO1
[MUST BE OTHER THAN ZERO
JPLS
MDAR'F
16
[TO DO PREDICTION SEQUENCE
ARMD
FDPTR
PROFL
JUMP 'I
169
PRO!:
STG3L:
SEG1:
ARtD
MDAR
ARMD
JPSR
ARMD
MDAE'L
-91940.!K
JPAN
MDAE'N
JPAN
ARMD
ARMD'O
JUMPI
$PPP
wY
$QQQ
$DISTC
STAGE
SEG3
SLOPE
SEG2
STG1
SEGIF
PROFL
IWAYPOINT
Y VALUE
[IN "FNST2"
[DISTANCE TO W.P. 823
[SUBTRACT DECELERATION
(DISTANCE
[LENGTH OF DESCENT PATH
[DIST TO GO IN LEVEL FLT
(IN SEG 2 COMPUTE THE DESCENT REQUIRED TO PLACE AIRCRAFT ON SLOPE
[AFTER 32 SECONDS OF TRAVEL (NO WIND)
SEG2:
SEG3:
MDAE
ARLS
ARBR'F
MDAR'N
ARRS
BRAE'F
ANAR
ARAR'H'N'F
MPYU
MDBR
ARLS
BRMD
MDAE'N
BRAE'F
ARLS
ANAR
ARMD
ARMD'O
JPSR
JUMP'I
MDAR
ARMD
ARMD'O
MDAR
ARMD
JUMP'I
SLOPE
3
$VT
5
ZERO
TANSL
$RB16
2
INITZ
FINZ
2
ZERO
VERGR
SEG2F
VBUGC
PROFL
STAGE
STG3
SEG3F
FINZ
INITZ
PROFL
[SLOPE DISTANCE 823
[TO B20R
[COMPUTE REQUIRED ALTITUDE
[32X'S VEL,810 = B15
(SHIFT TO B20
[SLOPE DIST REMAINING
[OR ZERO IF NONE
[AFTER 32 SECS
[COMPUTE ALT REQ AT THAT TIME
[SHIFT TO B16
[CHANGE INITIAL ALTITUDE
[+(-FINAL) = -REQ IN 32 SEC
(ADD CURRENT =ALT TO LOSE
[IN 32 SECS TO B14/32 = B9
[PREVENT CLIMB INDICATION
[COMMAND DESCENT FT/SEC 89
[REMAINING DISTANCE IN
[WHICH TO CHANGE SPEED
[FIX INITIAL ALTITUDE
170
[LINEARIZED MINIMUM AND MAXIMUM AIRSPEED CALCULATION
[FOR ANY ALTITUDE IN AR (B16)
MIN = 155 + .0055 H
H ABOVE 25K
[MAX = 517 - .1124 H
= 517 + .0084 (H-25K) BELOW 25K
[
ALL H
MI[WAS:
MIMA
:
MIMA2:
ARMD
MDAE'H'F
JPAN
ARAR'H'F
MPY I
JUMP
ARAR'H'F
MPYI
NOOP
MDAE'H'F
ARBR'F
MDAR'H
MPY I
NOOP
MDAE'H'F
JUMP 'I
4MMAL T
63625
MIMAI
(ALTITUDE
67551
MIMA2
[-.0024
36700
(.0089 KTS =
33243
[517 KTS = 874 FT/SEC B10
[RETURN MAXIMUM IN BR
MDBR
BRAR'F
MDAE'H'N'F
JPAN
MDAE'H'N'F
JPAN
MDAR'F
ARMD
JUMP
BRAR'H'N'F
MPYI
NOOP
ARMD'H
JUMP
BRAR'N'F
MDBR'H'N'F
ANIR
BRAE'F
ARAR'H'F
MPY I
MDBR
ANIR
BRAE'F
ARMD'H
JPSR
0
0
37777
JUMP 'II
IN AR B16
E-25000 FT 816
KTS
= -.004 FT/SEC
.015 FT/SEC B-6R
MMALT
22712
(,0055 KTS = .0092 FT/SEC B-6
10137
MIMAS
[155 KTS = 262 FT/SEC 610
[RETURN MINIMUM IN AR
VERGR
[COMMAND DESCENT
2052
LEVL1
4125
LEVL2
180.
VBANG
FINVB
(LESS THAN 2000 FT/MIN?
((33.33 FT/SEC) B9
[L.T. 2000+4000 FT/MIN
[(66.64 FT/SEC)
[ELSE LIMIT ROTATION
[TO 180 (METER PEGGED)
VBUGC:
LEVL1:
LEVL2:
FINVB:
VBANG:
VBSIN:
VBCOS
2546
(2.7 DEG ROTATION
[PER FT/SEC
VBANG
FINVB
2052
NEGBR
[ADD OR SUBTRACT
[33.3 FT/SEC
[DEPENDING ON SIGN
[OF V2
126:3
90DEG
NEGBR
(1.35 DEG ROTATION
[LIKEWISE ADD OR SUB.
(90 DEGREES
VBANG
$SNCSR
VBUGC
171
NEGBR:
NEGAR:
ZERO:
NZERO
FLAG i
PTAFL:
ITERf:
ITERC:
SEG IF:
SEG2F:
SEG3F:
PROTT:
STRBF CLCKF:
SDISF:
MINS:
WPTEM:
WPTRI:
WPTR2:
WPTR3:
WPTR4:
WPASP:
WPALT:
WPATA i
ASPI 0;
ALTD1 :0;
ATA1 :0;
WPR 16:
WPI2M:
LDALT:
LDASP:
WPSEL:
SELST:
TANSL:
COTSL:
INITZ:
FINZ:
FINTM:
FINAL:
FINAS:
WPX:
WPY:
STAGE:
STG1:
STG3:
SLOPE:
DCDST :
TOLER:
REACT:
ACCEL:
DECEL:
SPSET:
CMDSP:
ASO:
BRBR'N'F
ARAR'N'F
0
-0
0
-0
-0
0
0
0
0
-0
-0
-0
0
0
0
0
0
0
0
0
0
ASP2 : 0:
ALTD2:10;
ATA2: a;
0
0
0
0
0
0
6552 1H
4612! H
800. !K
2000.lK
7000 H
7000! H
0
0
0
ASP3: 0
ALTD3: 0
ATA3: 0
[TAN 3 DEG B-2
[COT 3 DEG 87
[TOLERANCE WITHOUT ITERATION
[REACTION DISTANCE
[ACCELERATION RATE FT/SEC**2
[DECELERATION RATE
172
VERGR:
VERRT:
CHNGR'
ERROR:
90DEG:
DFI:0;
NMALT:
SUM:
TAUl:
TAU2:
SIZE:
NN\TM\MM:
NN\AS\MM:
NN\D\MM:
NN\AS2:
NN\AVE:
NN\SLZ:
NN\TIM:
NN\TA:
NN\ASF:
FIN\NN:
HIBND:
LOBND:
[DATA BLOCKS
VLST:
0
401H
11IH 25252
0
90,!H
DF2:G;
0
0
0;
0;
0
IREPEAT
IREPEAT
0
ENDI
IREPEAT
0
0
ENDI
0
0
0
0
0
0
0
ENDI
0
0
DFT:0
TALUSI
TAU2S:
-110908,
-153054,
0
0
NN, (MX, MN)
MM,(0,1,2,3,4)
MM..(0,3)
-195520.!K
180140,!K
DLST:
[VERTICAL BUG RATE OF CHANGE
[SPEED BUG RATE OF CHANGE B10
!K
!K
EWAYPOINT DATA
[X LOCATION (GARDNER)
EY LOCATION
[(PROVIDENCE)
-25344. IK
114816, K
[(ACTON)
40000, !K
-62:345. !K
[(WHITMAN)
IREPEAT
-0
16!1H 0
MDOS
MD05
MD05
MD05
MD05
ENDI
NN. (0, 1)
CX OFFSET (15!H XXXXX)
[Y OFFSET
ID\NN
ALT\NN
SP\NN
TIM\NN
TRNGL
173
REFERENCES
1.
-2.
Report of the Air Traffic Control Advisory Committee, U.S.
Dep artment of Transportation, Vol.1, Deeember 1969.
Strategle Control Algorithm Development, Volume II: Technical
Boeing Commercial Airplane Co., Contract DQT-TSC-538,
Repgrt.
December 1973.
3.
Vietor, Carl W. "Time, Space, and Energy Management in the
Airways Traffic Control Medium", Journal of the Institute of
Navigation. Vol.20, No.2, pp. 159-169, Summer 1973.
4.
Hemesath, N.B., J.M.H. Bruckner and others. Three and Four
Dimensional Area Navigation Study Simulation and System Development.Collins Radio Co., CONTRACT DOT-FA72WA-3123. April 1974.
5.
Vertical Area Navigation System
Bolz, E.H. and E.D. McConkey
Analysis. Champlain Technology, Inc., Contract no. DOT-FA72WA2831, September 1972.
6.
CONNELLY, MARK E. The Role of the Airborne Traffic Situation
Display in Future ATC Systems. Electronic Systems Lab. Report
ESL-P-483, May 1972.
7. Morgenstern, Bruce R. Evaluation of the Airborne Traffic Situation Display as a Backup Terminal ATC device. S.M. Thesis,
Dept. of Aeronautics and Astronautics, M.I.T., December 1974.
8. Jet Transport Performance Methods. The Boeing Co.,
May 1969.
Airplane Group, Seattle.
9.
Commercial
Janes All the Worlds Aircraft 1973-74, McGraw-Hill Book Co.,
New York.
John Wiley
10.
Etkin, Bernard. nynami en onf Atmonpheri e Flight.
and Sons, Inc., New York. 1972.
11.
Connelly, Mark E. Simulation of Aircraft.Electronic Systems
7591-R-1. February 1959.
Lab. Report,
12.
Connelly, M.E. and 0. Fedoroff. A Demonstration Hybrid Computer for Real Time Flight Simulation. Aerospace Medical Research
Laboratory, USAF. Report no. AMRL-TR-65-97. June 1965.
13. Hill, P.G. and C.R. Peterson. Mechanics and Thermodynamics of
Propulsion. Addison-Wesley Publishing Co. Inc., Reading, Mass.
1965.
174
REFERENCES
(CONT'D)
14.
U.S. Government Printing
U.S. Standard Atmosphere, 1962.
December 1962.
Office, Washington, D.C.
15.
707 Operating Manual.
American
16. Programming Instruction Manual:
Adage, Inc., Boston, Mass.
Airlines.
June 1974.
Adage Graphics Terminal.
A VTOL Prediction Display.
17. Kemp, G.G.
Thesis, Department of Aeronautics
S.M. and E.A.A.
Astronautics, M.I.T. September 1969.
and
18. Anderson, R.E. Format Evaluation for an Airborne Air Traffic
S.M. Thesis, Dept. of Aeronautics and
Situation Display.
Astronautics, M.I.T. June 1971.