The influence of several parameters on the time required to fly a nominal profile descent of a B-737 from an entry fix to a metering fix 75 n.mi. away was studied. The ground distance for the constant speed segment was adjusted in each case so that the aircraft would always arrive at the metering fix position at the completion of the five segments of the profile descent. The influence of eight parameters on the same nominal profile descent is outlined, but the method used for the off nominal cases was changed. The time calculated for the constant speed segment in the nominal case is used for all off nominal cases. This method allows the aircraft to arrive at the metering fix before or after the profile descent is complete. It is shown that descent Mach number and wind speed have a large effect on the time error, whereas weight was a much smaller effect

Dejarnette, F. R.

English

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(NASA-CR-172338-Add) ELFPCTS OF AIRCRAFT
AWD FLIGHT PARAMETERS ON ENEGGY-EFFICIENT
PROFILE DESCENTS IN TIME-BASED METERED
TEAFFIC (Research Triangle Inst.) 19 p
HC A02/MF A01
	 CSCL 17G G3101
RESEARCH TRIANGLE INSTITUTE
RTI/2467	 Addendum to NASA CR-172338
4D
	 0
EFFECTS OF AIRCRAFT AND FLIGHT , PARAMETERS
ON ENERGY-EFFICIENT PROFILE DESCENTS IN
TIME-BASED METERED TRAFFIC
by
®	 Fred R. DeJarnette
Center for Systems Engineering
Research Triangle Institute
Research Triangle Park, North Carolina 27709
6
for
NPSA
National Aeronautics and Space Administration
Langley Research Center
Hampton, Virginia 23665	 L^$^
41) t5
Date of Original Report: February, 1984	 N r
®	 Date of Addendum:	 November, 1984	 c' 
.1)^F	
0Q
POST OFFICE BOX 12194 RESEARCH TRIANGLE PARK, NORTH CAROLINA 27709
0
0
0
DF
stops and Segment 2 begins. Still maintaining idle thrust and a clean con-
figuration, the aircraft descends at constant CASd until the metering-fix
altitude is reached. Segment 1 is a deceleration at constant altitude
(hmf) from CASd to the designated metering-fix calibrated airspeed
(CASmf).
Section 4.1.1 in NASA CR-172338 describes the influence of the follow-
ing parameters on the time, At 
TOPto fly from the entry fix to the
metering fix: metering fix altitude (h mf), descent Mach number (Md),
descent calibrated airspeed (CASd), cruise altitude (hc), cruise Mach
number (Mc), ground distance (ASTOT)'and aircraft weight (W). A
nominal case for the 8-737 was chosen and the separate effects of these
parameters on 
otTOT 
were calculated by changing each parameter by a
prescribed amount while holding all the other parameters fixed at the
values for the nominal case. A significant feature of the method used in
those calculations was that the ground distance for Segment 4 (the constant
speed segment) was adjusted in each case so that the aircraft would always
arrive at the metering-fix position at the completion of the five segments
of the profile descent. The aircraft would have the same airspeed and
altitude as the nominal case, but the off-nominal cases would not arrive at
the time predetermined for the nominal case. Thus, for the off-nominal
cases, the uncertainty or error in each parameter investigated was known
before the profile descent flight path was calculated so that the ground
distance in Segment 4 could be adjusted to allow the aircraft to arrive at
the metering fix position at the completion of the five segments of the
profile decent.
NEW ANALYSIS
As a supplement to the information in NASA CR-172338, this addendum
gives additional results on the influence of parameters on profile
descents. In the present results additional parameters are considered and
the method used to calculate the off-nominal cases was changed so that the
ground distance in Segment 4 is not adjusted to allow the aircraft to
arrive at the metering fix at the completion of the five segments of the
profile descent. Instead, the time calculated for Segment 4 (ot4) in the
nominal case is used for all off-nominal cases. This means that the air-
craft may arrive at the metering-fix ground position before the profile
descent is complete (early arrival), or it may complete the profile descent
2
before the metering fix is reached (late arrival). The method used to cal-
culate the time (nti) and distance (nSi) for each segment of the pro-
file descent is the same as that described in NASA CR-172330 except for
Segment 4 in the off-nominal cases. For the off-nominal cases, the time
n4 is the same as that for the nominal case, and since the airspeed and
wind are constant in Segment 4, the distance nS4 is obtained from
eq. (27) in NASA CR-172338 as
nS4 = nt4 ( V 4 + VW cos( e- ^w))I
For late arrivals, the aircraft is flown at the prescribed metering
fix altitude (hmf) and airspeed (CASmf) from the position of com-
pletion of the profile descent to the metering fix ground position. This
3	 additional segment requires engine thrust above idle thrust in order to
maintain constant altitude and airspeed. Consequently, the fuel flow rate
is higher than that for idle thrust. When arriving at the metering fix the
aircraft has the correct airspeed and altitude, but the time required is
0	 longer than that for the nominal case. The distance error is defined as
the ground distance between the position where the profile descent was com-
pleted and the metering fix.
For early arrivals, the aircraft reaches the metering fix ground posi-
tion before all of the profile descent segments have been completed. If
the aircraft is still decelerating in Segment 1 when it arrives at the
metering fix, it will have an error in its airspeed and time of arrival but
its altitude is correct. If the aircraft is still in Segment 2 or 3 when
D	 it arrives at the metering fix, it will have errors in airspeed, altitude,
and time of arrival. The distance error for early arrivals is defined as
the ground distance from the metering fix to the position where the five
segments of the profile descent would have been completed if the profile
descent were continued beyond the metering fix position.
D
a
	
3
i
RESULTS AND DISCUSSION
The nominal case used here is the same B-737 profile descent used in
Section 4.1.1 of NASA CR-172338. The prescribed parameters are:
W	 = 87,500 lb
he	 = 35,000 ft
Mc	 = 0.78
Md	 = 0.67
CASd = 265 knots
hmf = 19,500 ft
CASmf = 250 knots
ASTOT = 75 n.mi
otREQ = 699.54 sec
Standard day and no wind
Although the values of CASd and etREQ differ slightly from those
used to calculate Table 4-3 in NASA CR-172338, the values actually used for
the nominal case in Section 4.1.1 were the same as those listed above. The
calculated time and distance for each segment of the nominal case are:
SEGMENT
	
1	 2	 3	 4	 5	 TOTAL
eSi(n.mi)	 1.465	 24.461	 21.011	 21.343	 6.719	 75.00
oti(sec)	 15.38	 234.52	 192.66	 198.87	 58.11	 699.54
Metering fix crossing errors in ground distance, time, altitude, and
calibrated airspeed have been calculated for off-nominal cases due to
errors in the following parameters:
i
PARAMETER	 ERROR RANGE
Weight, W	 + 40,000 lb
Cruise Altitude, he	 + 1,000 ft
Cruise Mach number, Mc 	 + 0.08
Descent Mach number, Md	 + 0.02
Descent Calibrated Airspeed, CASd	 + 10 knots
Wind Speed, Vw	 + 20 knots
Wind Speed Gradient, dVw/dh	 + 0.008 knots/ft
Atmospheric Temperature Bias	 + 20°F
4
rw
fThe wind-speed used in the wind-speed gradient cases was determined from
the requirement that the average wind-speed between the cruise and meter-
ing fix altitudes was zero. Each off-nominal profile descent was calcu-
lated using the same input parameters as the nominal case, except for the
specific off-nominal parameter considered. The results for the metering
fix crossing errors due to errors in the eight parameters listed above are
'	 plotted in Figures A-1 through A-8. These figures show the altitude error,
airspeed error, time error, and distance error when the aircraft crosses
the metering fix ground position. Note that the distance error is the
distance between the metering fix and the ground position when all segments
of the profile descent are complete.
Table A-1 lists metering fix crossing errors in time, distance, and
airspeed due to specfic variations in the eight parameters considered. An
error in descent Mach number of only ±0.01 would produce a time error of +6
sec at the metering fix, whereas an error of +5,000 lb in weight would
cause only an error of +0.64 sec in time (a -5,000 lb weight error would
cause a time error of -1,39 sec). Without wind and atmospheric temperature
errors, the combined errors of the other 5 parameters could cause time
U	 errors between -11.20 sec and +9.97 sec for a nominal time of 700 sec,
distance errors from -3.33 n.mi. to 2.73 n.mi. for a nominal value of
75 n.mi., and airspeed errors up to 23.63 knots for the nominal 250 knots
at the metering fix. As expected, wind speed has a significant influence
on the time. A variation of 4•5 knots produced time errors from -10.14 sec
to +10.65 sec. Wind-speed gradient and atmoshperic temperature errors
produced much smaller time errors. Table A-1 shows that a combination of
all the errors considered could produce errors in time from -27.78 sec to
26.78 sec, distance errors from -4.85 n.mi. to 4.25 n.mi., and airspeed
errors up to 39.19 knots.
Table A-2 shows the change required in each parameter, separately, to
produce an error of ±1 sec in the metering fix crossing time. In addition
to the eight parameters considered previously, the effects of metering fix
altitude and distance from entry fix to metering fix are shown also.
Errors in descent Mach number from -0.0017 to 0.0018 can produce time
errors of +1 sec, and wind speed errors from -0.400-9 knots to 0.493 knots
9	 can produce errors of +1 sec in time. On the other hand, a change of
-3,603 lb to +7,829 lb in weight is required to change the time +1 sec. In
5
addition, Figure A-1 shows that a weight error of -20,000 lb produces a
time error of -7 sec and an error of +20,000 lb causes only 1.6 sec error
in time.
CONCLUSIONS
For a nominal profile descent of a B-737, it was found that errors in
descent Mach number and wind speed produced large errors its the time
required to cross the metering fix. Errors in weight were found to cause
relatively smaller errors in time. However, these conclusions could change
significantly for nominal profile descents different from the one con-
sidered here.
4
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a
6
6C.
g
TABLE A-1
ERRORS IN CROSSING METERING FIX DUE TO VARIATION IN PARAMETERS
PARAMETER VARIATION TIME ERROR DISTANCE ERROR AIRSPEED ERROR
sec (n.mi.) (knots)
Cruise Alt. 250 ft +0.70 -0.75 7.65
(35,000 ft.) -250 ft -0.84 +0.75 0
6
Cruise Mach No. +0.01 +1.27 -0.47 4.80
(0.78) -0.01 -1.47 +0.55 0
Descent Mach No. +0.01 +6.00 +0.10 0
(0.67) -0.01 -5.98 -1.14 1.50
Descent CAS +2.5 kts +1.36 +0.27 0
(265 knots) -2.5 kts -1.52 -0.28 +2.89
Weight +5000 lb +0.64 -0.69 6.79
(87,500 lbs) -5000 lb -1.39 +1.06 0
WORST CASE(without wind and temp) +9.97 +2.73 +22.63
-11.20 -3.33 -0
Wind Speed +5 knots 10.65 -0.97 +9.79
4 (0 knots) -5 knots -10.14 +0.97 -0
Wind Speed Gradient +5kts/103ft 2.52 -0.24 +2.62
(0 knots/ft) -5kts/103ft -2.71 +0.24 0
Atmospheric Temp. Bias +5°F +3.64 -0.31 +3.15
(59°F at S.L.) -5°F -3.73 +0.31 0
WORST CASE(including wind and temp) +26.78 +4.25 +39.19
-27.78 -4.85 0
NOTE:	 For the parameters above, no altitude errors were found.
7
TABLE A-2
p
^I
I
CHANGE IN PARAMETERS TO CHANGE TIME +ONE SEC.
PARAMETER PARAMETER CHANGE REQUIRED TO
CHANGE TIME
+ONE SEC. -ONE SEC.
Cruise Alt. -299 +358 ft
Crui-se Mach No. -0.0068 +0.0079
Descent Mach No. -0.0017 +0.0018
Descent Calibrated Airspeed -1.65kts +1.84kts
Metering Fix Altitude +765 ft -1372 ft
Distance from Entry Fix +0.093 n.mi -0.093 n.mi
to Metering Fix
Weight -3603 lb +7829 lb
Atmospheric Temperature Bias -1.34°F +1.37°F
Wind Speed -0.469kts +0.493kts
Wind-Speed Gradient -0.199kts/103ft +0.185kts/103ft
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< N 0N
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30	 50	 70	 90	 110	 130
14EiGHT (1000 lbs.)
Figure A-1. Crossing Errors At Metering Fix Due To Weight
Variation.
10
YD
D
1000+.
w4.
o	 ..
^CIE is
.^ o x
w	 0
0:	 20
ID I
HD	
w 
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w VO
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F C
-5
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cdCD w 5LL
w w
w•= p
-5
••
o
c.
34000	 35000	 36000
CRUISE ALTITUDE, ft
Figure A-2. Crossing Errors At Metering Fix Due To Cruise Altitude
IL	 Variation.
11
400
a 200^o
^
..
x
w _
0
20
g ¢ 10
v
0
I
1
c	 I
.^ 10
YJ
o 5 ^_-
c v .^
W C0 0
W UX N n
-5
V -10
5
c
C) wz
w w 2.5
W •r
aE
Z
C N
0
VI
Ln
Q
Q .°: -2.5
0.70	 0.74	 0.78	 0.82	 0.86
CRUISE MACH NUMBER
Figure A-3. Crossing Errors At Metering Fix Due To
Cruise Mach Number Variation.
E
12
wo^ ..
J 
ce 
z•Qw
6
10
J
G'
c Ul
w C0
w UE ai
^, ^1..	 w
s
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-10
-159
0
f
t
f
6
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m0c
wx v
9
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4
P
c +^o
KLUi.
w w
w• MU E
G C LnLnQ
•-.	 90
1	 1	 e	 1	 1
0.65	 0.66	 0.67	 0.68	 0.69
DESCENT MACH NUMBER
Figure A-4. Crossing Errors At Metering Fix Due To
Descent Mach Number Variation.
0.5
0
-0.5
13
aW y
~
°
a
,.
c 200 *`
.r O ..
v 0^	 l^¢U
m 10I0
wLOw +^ ¢
	
5
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a z	 5
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J -5
-10
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w w 0
w m
H e N - 1
N Q
•r	 p,
°	
-2
	
1	 I	 I	 1	 1
255
	 260	 265	 270	 275
DESCENT CAS, kts
Figure A-5. Crossing Errors At Metering Fix Due To
Descent Calibrated Airspeed Variation.
14
I
40
r
20
CDUl 0w0 ^. 0U
W (V -.
N^— a -20Jv
-40
..D
D
D
D
D
D
4.
4N	 1000
W
o	 Soorm xJ 1 vC W
	 D
x	 20oz
w Y ^
in	
10
w
0
I
w wC) zz o
x w
w w
w m•E .^Z E .`.
V) c v~i
CL
a .^
i	 i	 i	 1	 ,
-20	 -10	 0	 10	 20
(HEADWIND)	 (TAILWIND)
WINDSPEED, kts
Figure A-6. Crossing Errors At Meterf a ^fx Due To Wind
Speed Variation.
D
5
0
.5
of
15
SUMMARY
► 	 In NASA CR-172338 results viere presented for the influence of several
parameters on the time required to fly a nominal profile descent of a B-737
from an entry fix to a metering fix 75 n.mi. away. A significant feature
of the method used in those calculations was that the ground distance for
the constant speed segment was adjusted in each case so that the aircraft
would always arrive at the metering-fix position at the completion of the
five segments of the profile descent. This addendum gives the influence of
eight parameters on the same nominal profile descent, but the method used
>	 for the off-nominal cases was changed. In the present results the ground
distance in the constant speed segment is not adjusted as done previously.
Instead, the time calculated for the constant speed segment in the nominal
case is used for all off-nominal cases. This method allows the aircraft to
arrive at the metering fix before (early arrival) or after (late arrival)
the profile descent is complete. The results show that descent Mach number
and wind speed have a large effect on the time error, whereas weight had A
much smaller effect.
P
BACKGROUND
In the subject contractor report, NASA CR-172338, a computational
y	 algorithm is described for calculating the flight path information needed
to fly from an entry fix through a profile descent to a metering fix and
arrive there at a predetermined time, altitude, and airspeed. The five
segments of the profile descent are illustrated in Figure 1-1 (repeated
► 	 herein) as well as four additional segments for the flight path from the
metering fix to the aim point. The segments are numbered in the reverse
order from which they occur. Segment 5 starts at the entry fix with cruise
.altitude (hc) and Mach number (Mc) and decelerates at constant altitude
with idle thrust until the prescribed descent Mach number (Md) is
reached. Segment 4 is a constant speed and altitude path to the beginning
of descent. In Segment 3 the aircraft descends with idle thrust and a
clean (low drag) configuration at an attitude which maintains '-)nstant
Md. As the altitude decreases, the calibrated airspeed increases. When
the calibrated airspeed reaches a prescribed value (CASO , Segment 3
C,^
co N
CZx
W p
W U
LUCl ¢¢
~ ^ J
I
i
60
40
20
0
-20
-40
16
w
1000
W 4^^•o ..
so" cT^3	 500
V¢w 0 —
20z0
w ¢ 10 4
LLN
..
0
K W
CD w
s o
w w
W m
Z E
¢ c F-R NN ¢
..-.	 q
im
L^	 1	 1	 1	 __J
-8	 -4	 0	 4	 8
WIND GRADIENT ( kts/1000 ft)
Figure A-7. Crossing Errors At Metering Fix Due To Wind
Speed Gradient Variation.
0
-5
^`	 I
t
9
i
9
8
w v-
^a =
GIs
¢w
w 20Q
..H
i¢ 10vw.X
`^ v 0
20
al
10
z9
cw O 0	 ^-U _
E y w
J -10
-20
2
c w
	
aC) 0
	 1
w w
'co 0
z E¢ c h
1- N
	
a	 -1
o ..
40	 50	 60	 70	 80
SEA LEVEL TEMPERATURE, °F
Figure A-8. Crossing Errors At Metering Fix Due To
Temperature Bias Variation.
1
,
17
'if.
I
I
^i
D
Mi
'Addendum to 7. Government Acces,ion No. 3, Recipient's Catalog No.
NASA CR-172338
4, Tole and Subtitle 5, Repon Date
Effects of Aircraft and Flight Parameters on Energy- November, 1984
6. Performing organization CodeEfficient Profile Descents in Time-Based Metered
Traffi c
7, Autharls) 6. Performing Organization Report No,
Fred R. DeJarnette RTI/2467
10, Work Unit No,
9. Per formingorganizatlon Name and Address
Research Triangle Institute 11, Contract or Grant No,
P.O. Box 12194
Research Triangle Park, NC 	 27709 NAS1-17023
13, Type of Report and Period Covered
12. Sponsoring Agency Name and Address
National Aeronautics and Space Administration
Contractor Report
14, Sponsoring Agency CodeWashington, D.C.	 20546
15. Supplementary Notes
Langley technical monitor: 	 Leonard Credeur
16. Abstract
In NASA CR-172338 results were presented for the influence of several para-
meters on the time required to fly a nominal profile descent of a B-737 from
an entry fix to a metering fix 75 n.mi. away. 	 A significant feature of the method
used in those calculations was that the ground distance for the constant speed
segment was adjusted in each case so that the aircraft would always arrive at the
metering fix position at the complexion of the five segments of the profile descent
This addendum gives the influence of eight parameters on the same nominal profile
descent, but the method used for the off-nominal cases was changed.	 In the present
results the ground distance in the constant speed segment is not adjusted as done
previously.	 Instead, the time calaculated for the constant speed segment in the
nominal case is used for all off-nominal cases. 	 This method allows the aircraft
to arrive at the metering fix before (early-arrival) or after (late arrival) the
profile descent is complete.	 The results show that descent Mach number and wind
speed have a large effect on the time error, whereas weight had a much smaller
effect.
17, Key Words (Suggested by Autharls)) 18. Distribution Statement
Profile Descent
Metered Traffic Unclassified - Unlimited
19. Security Classlf. (of this report) 20. Security ClassiL (of this page) 21. No. of Pages 22.	 Price
Unclassified Unclassified 18
aoos	 For sale by the National Technical Information Service, Springfield, Virginia 22161
18


Effects of aircraft and flight parameters on energy-efficient profile descents in time-based metered traffic

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