scale model pattern measurements of aircraft l-band ......faa-rd-75-23 project report atc-47 scale...
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FAA-RD-75-23
Project ReportATC-47
Scale Model Pattern Measurements
of Aircraft L-Band Beacon Antennas
K. J. Keeping
J. C. Sureau
4 April 1975
Lincoln Laboratory MASSACHUSETTS INSTITUTE OF TECHNOLOGY
LEXINGTON, MASSACHUSETTS
Prepared for the Federal Aviation Administration, Washington, D.C. 20591
This document is available to the public through
the National Technical Information Service, Springfield, VA 22161
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This document is disseminated under the sponsorship of the Department of Transportation in the interest of information exchange. The United States Government assumes no liability for its contents or use thereof.
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1. Report No.
FAA-RD-75-23
2. Goyernment Accession No.
Technical Report Documentation Page
3. Recipient's Cotalog No.
4. Title and Subtitle
Scale Model Pattern Measurements of AircraftL-Band Beacon Antennas
7. Author( s)
K. J. Keeping and J. C. Sureau
9. Performing Orgonizotion Name and Address
Massachusetts Institute of TechnologyLincoln LaboratoryP. O. Box 73Lexington, Massachusetts 02173
12. Sponsoring Agency Name and Address
Department of TransportationFederal Aviation AdministrationSystems Research and Development ServiceWashington, D. C. 20591
15. Supplementary Notes
5. Report Date
4 April 1975
6. Performing Orgoni zation Code
8. Performing Organization Report No.
ATC-47
10. Work Unit No. (TRAIS) 45364Project No. 034-241-012
II. Contract or Grant No.
DOT-FA72-WAI-261
13. Type of Report ond Period Coyered
Project Report
14. Sponsori ng Agency Code
The work reported in this document was performed at Lincoln Laboratory, a center for researchoperated by Massachusetts Institute of Technology.
16. Abstract
nus report describes the techniques and apparatus used to measure the directionalpatterns of aircraft ATC transponder antennas (L-Band) using digital techniques andmagnetic tapes for data storage. Algorithms involved in data normalization, crosspolarization correction and coordinate conversions are discussed. Some typicalapplications of the data are illustrated with actual computer outputs obtained from themodel measurements.
17. Key Wards 18. Distribution Statement
• Aircraft antenna patternsATC antenna patternsScale model measurements
Document is available to the public throughthe National Technicallnformation Service,Springfield, Virginia 22151.
19. Security Clauif. (of this report)
Unclassified
Form DOT F 1700.7 (8-72)
20. Security ClalSif. (of this page)
Unclassified
Reproduction of completed page authorized
21. No. of Pages
AIR FORCE (1) MAY 8, 1975--355
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..
..
ACKNOWLEDGMENTS
The work reported in this paper was begun by Dr. John Ruddy who
did the initial planning, set up the procedures for obtaining accurate aircraft
scale models, and participated in selection of the antenna range instrumentation.
Earl Hunter operated the antenna range apparatus. Ms. Kathleen Knox did the
necessary computer programming which proved to be a very frustrating job
due to initial equipment problems and to insidious machine-language problems
that took a great deal of time and consultation to clean up. Many conversations
with Dr. William Harman and Gary Schlieckert were of great use in directing
the overall program. Without the assistance of all of the above and of Group 61
and Group 28 personnel, this work could not have been successfully carried out .
iii
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•
Section
I
II
III
Appendix A
Appendix B
Appendix C
TABLE OF CONTENTS
Introduction
Description of Equipment and MeasurementsTechniques
Data Normalization and Processing
Aircraft Models and Antenna Positions
Principal Plane Patterns
Cros s - Polarization Los s and CoordinateConversion
Bibliography
LIS T OF ILLUS TRATIONS
Page
1
2
9
16
50
138
143
Figure
1
2
3
.. 4
5
Aircraft model on antenna positioner
Block diagram of Scientific Atlanta model1892 magnetic tape recording system
Photograph of Scientific Atlanta model 1892magnetic tape recording system
Model aircraft and tower geometry
Lear jet bottom-mounted front,flaps down, wheels up
v
Page
4
5
6
8
11
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Figure
6
7
A .1(a)(b)and(c)through
A .1 1(a)(b)and(c)
B. 1 -1throughB.11-11
LIST OF ILLUSTRATIONS (cont.)
Radiation density contours for Lear jet(wheels up and flaps down; antenna in bottomfront position)
Typical probability distribution function forantenna gain
Aircraft views: (a) 3/4 view, (b) top view,and (c) bottom view
Tape data of principal plane patte rns for theevaluated aircraft
vi
Page
13 ..
,
15
17through
49
51through
137
..
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•
..
SCALE MODEL PATTERN MEASUREMENTS
OF AIRCRAFT L-BAND BEACON ANTENNAS
I. INTRODUCTION
The Technical Development Plan for DABS discus ses, under the heading
of design options [Ref. 1], the possibility of aircraft antenna diversity as a means
of ove rcoming the limitations on system performance arising from nulls in air
craft antenna patterns. Under Phase I of the DABS Development Plan it also
calls for a program of aircraft antenna pattern measurements [Ref. 2] with
special attention being given to general aviation aircraft for which little infor
mation is available.
Accordingly, a program was initiated at Lincoln Laboratory to obtain
these pattern data in the most convenient form for use in further studies. The
directional gain of aircraft antennas was to be measured over a complete
spherical surface with uniform density, and the number of measurements was
to be great enough so that all significant pattern data would be recorded.
These data must cover a variety of typical flight conditions (such as wheels
up, wheels down, and flaps up, flaps down, etc.). Various possible antenna
locations on the aircraft should be used so that comparisons can be made as
to the relative suitability of the position considered. Clearly, diversity
schemes must be based on such comparative data •
1
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II. DESCRIPTION OF EQUIPMENT AND MEASUREMENTS TECHNIQUES
There are many reasons, which will not be enumerated here, that it is
impractical to make antenna measurements on a full scale aircraft. Consider-
ing the position apparatus, which was available to hold the model aircraft at
accurately known angular coordinates while the measurements are made, it
appeared that the maximum dimension of the model should not exceed about
30 inches. Consideration of actual dimensions of general aviation aircraft
indicated that a scale factor of 1/20 would be suitable. Since the actual fre-
quency of the proposed DABS system is 1060 ± 30 MHz, this means that the
pattern measurements must be carried out at 20 X 1060 = 21200 MHz = 21. 2
GHz (wavelength::::: o. 56"). Although the antenna gain itself is very low, the
whole aircraft (fuselage, wings, etc.) makes up a very complex antenna struc-
ture and, to assure that the measured patterns would be like those that would
be seen at "infinite distance II from the model aircraft, it was decided that the
distance separating the antenna, used to illuminate the model on the positioner,
should be large compared to 2D 2/A where D is the maximum dimension of the
model. Since D is approximately 30 inches, the required length of themax
antenna range is about 270 feet. The available range length of 2000 feet is
clearly more than adequate.
Through the cooperation of the manufacturers, loft line drawings were
obtained for the following types of general aviation aircraft:
The Lear JetPiper "Cherokee II 140Shrike "Commander"Cessna 150Cessna "Cardinal"Ces sna "402B"Beech "Baron"
Beech "B -99"Twin OtterHelio VlODGrumman Gulfstream II
2
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•
•
Scale models (1/20 scale) were obtained of each type. These models
have dimensional tolerance of ±O. 30" with rigging tolerance no greater than
±0.060". Thus the largest dimensional errors are just over ±O. 1 wavelength
and as such should be of negligible importance, since the pattern of a flying
aircraft is difficult, if not impossible, to define exactly due to surface flexures
and vibrational modes. The actual form of the aircraft is a function of time
and it may never exactly regain any form it had in the past.
The aircraft models have removable wheels (where appropriate) to sim
ulate wheels -up conditions and removable flaps. They also have hollow fuse
lages with several antenna locations at or near the upper and lower center
lines; these antenna locations are shown in more detail in Appendix A. In
addition to this an adapter plate is fixed on the top and bottom of the fuselage
to permit attaching the model to the positioner.
The site of the aircraft models during measurement was probed before
making any measurements and it was found that the field intensity was constant
within ±O. 1 dB over the area to be occupied by the aircraft model during mea
surement (see Fig. 1).
A simplified block diagram of the overall data gathering facility is shown
on Fig. 2. The analog-to-digital converters used for angle readout make use
of synchro-to-digital conversion having a stated accuracy of 0.01 degree and
a resolution of 0.01 degree. Thumbwheel offsets are provided as a conven
ient means of zeroing the readout to correspond to any desired reference angle.
The analog-to-digital converter used for amplitude ratio readout pro-
vides either logarithmic or linear outputs. With the logarithmic option, the selected
sampling has a dynamic range of 85 dB and an accuracy and resolution of read-
out of O. I dB. The associated tape recording system is shown on Fig. 3.
3
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Fig. 1. Aircraft model on antenna positioner 4
•
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ATC-47 (2)
Transmitter
(2000 feet from rest of equipment)
•aircraftmodel
"'~ antenna Referencechannel antenna
and mixer
ModelPositioner
mixerin model
, 1coax through 2'rotary joints inpositioner A .0
eJ
TwoChannelReceiver
,AlB
- - - - - - - - --~~--
7 ·TrackTapeRecorder
AIDConverterAmplitudeRatio AlB
.~I_____J
AIDConverter
AIDConverter
r------I
/I
(:
r-~I
II
I/
I/
(Il
~IIIIII
DigitalPositionerProgrammer
•Tape Coupler
(Master Clock) ...... ~ Title ControlUnit
Trigger Pulses from Master Clock indicated with Dashed Lines
Fig.2-Simplified Block Diagram of Model 1892 Magnetic Tape RecordingSystem (Scientific Atlanta) and associated equipment.
5
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P13
0-59
0
Fig
.3
.S
cie
nti
fic
Atl
an
taM
od
el
18
92
Mag
neti
cT
ap
eR
eco
rder
Sy
stem
/
••
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•
The dual channel or phase amplitude microwave receiver (Scientific-
Atlanta Series 1750) has a dynamic range of 60 dB and amplitude accuracy of
±o. 25 dB. The output signal is modulated at 1000 Hz. The receiver supplies
isolated local oscillator power to two external mixers (in this application one
mixer is located in the aircraft model and the receiver accepts 45 MHz IF sig-
nals generated in these external mixers.
A description of the coordinate system and the detailed manner in which
pattern data are actually measured is shown in Fig. 4. The pole of the spheri-
cal coordinate system is the yaw axis of the aircraft. The <I> coordinate, and
angular rotation about the yaw axis, are then measured as indicated.
To record a complete data set, the antenna positioner was set so that
oe = 1 and <I> = O. The title word (described later) was first written on the tape.
The model was revolved about the yaw axis at a uniform speed and data were
sampled every 2 degree s in <1>. These data consist of e, <1>, and amplitude ratio
in dB. (This is the ratio of the signal received in the model aircraft antenna
to that received in the reference antenna.) Thus, 180 sets of angular and
amplitude data are recorded in the initial record. The record word is written
just after the title word, before the data were written. At this point the angle
<I> was stopped at zero and the angle e was advanced to 30• The new record
word was written, followed by 180 sets of data words, and so on until 90 com-
plete records had been recorded. This resulted in 90 X 180 = 16200 points in
the complete spherical coverage for which data had been measured.
The description just given applies for top mounted antennas. Bottom
mounted antennas require that the model be mounted in the inverted position
on the antenna positioner. Therefore, the first record on the data file corre-
o 0sponds to e = 179 and the 90th record corresponds to e = I •
7
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•
ep =00
(
~ep =900
~ INCIDENT FIELDHORIZONTALLYPOLARIZED
l18-4-16998L
YAW AXIS OF AIC
~8 ep=180°
•
8= 1800
8 =2700 -----E----------",..=-------t-- 8 =900
Fig. 4. Model aircraft and tower georn.etry.
8
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III. DATA NORMALIZATION AND PROCESSING
This process edits out the unnecessary angle data and produces the
amplitude data in dB with respect to isotropic on a 9-track tape. Now each
file consists of a title word and 16200 words of amplitude data.
The normalizing process is a numerical integration described below:
Let X be a two-dimensional array containing all of the unnormalized ampli-mnth th
tude data at the m value of <p and the n value of 8. Let there be N equal
intervals in the range of 8 between 0 and TT, and let there be M equal intervals
in <p between 0 and 2TT.
level,
Now, if A is the corresponding unnormalized powermn
•
X ron
A = 10 -nrmn
and Ae = Nand A¢ = ~
The total radiated power is the sum of all contributions through each ele-
mentary unit area (sin 8 A e A <p)
M N
•• P t = L L Amn sin(~)(~) (~)m= 1 n= 1
2 M N
=(~~) 2: 2 A mn sin(~)m=l n=1
9
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and to determine the average power radiated per steradian of surface we
divide by 4rr
M N
< P > =(2~M) 2: 2: A mn sine~nm= 1 n= 1
This is the isotropic level of the antenna radiation and in our case where
"N=90andM=180
180 90
< P >= (2X16~ 200t 2.. 2: A mn sin(~IT) .m= 1 n= 1
Note that when the A r are all unity, <P> = unity also, as it must for anmn s
isotropic radiator.
Now if~ mn represents the r'normalized" amplitude data expressed in dBmn
and X the unnormalized data,mn
x-- mn = X - 10 10glO <P> dBi.mn mn
The production of principal plane "omnidirectional" H plane, and E plane
cuts is clearly a very simple proces s when the normalized 9 -track data are
available (see Fig. 5a). It is important to take note of whether it is a top
mounted or bottom mounted antenna; then the omnidirectional data required
are either from the 45th or 46th record, i.e., at e = 89° or e = 91 0 • In the
complete file this corre sponds to data words from 2700 to 2880 or from 2880
to 3060, respectively. The E plane patterns are only slightly more involved.
All data for which <j> = 0.00
and <j> = 180.00
are required for the E -plane cut
10
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QO.NOSE:
" .RIGHT WING
PHI = 0
180L '80 ... • •• 0 0• TT T
••
2iO 90.0PHi = li:!O
(a) horizontal plane (b) wing to wing
90,0NOSH
PHI = 9C
•
lB • • .. ,• ..0TT0
•
90.0PH I = 270
(c) nose to tail
IATC-47(5) LFig. 5. Lear jet bottom-mounted front. flaps down. wheels up
11
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containing the wings (see Fig. 5b), and all data for which ep = 900
and ep = 270.00
are required for the E-plane cut containing the nose and tail (see Fig. 5c). A
complete set of principal plane patterns for those aircraft that were actually
measured (the measurements program was about 75% completed before being
stopped) is given in Appendix B.
Radiation density and contour plots are, in principle at least, quite
straightforward. There are available computer routines which, given data
measured at various points in a plane, can linearly interpolate and draw in
the contours of constant intensity. Such a program was used but, due to the
very large amount of data, the computing time was considered to be excessive
and unwarranted, considering the limited interest in this type of data presenta
tion. A very much simpler and cruder approximation to an accurate contour
plot is obtained by quantizing the data and printing out on a rectangular grid
the resulting data, going from left to right on each scan line and printing a
symbol only if the radiation level has shifted to some other quantized level.
While this is simple and required very little computer time, it does require
a great deal of patience and time to draw in the contour by hand later on. An
example of this process is given in Fig. 6.
Other applications of the data involving arbitrary maneuvers of the air
craft and the effective antenna gain to vertically-polarized radiation from a
beacon interrogator on the ground clearly involve coordinate transformation
and, since roll and pitch angles are permissible for the aircraft, cross
polarization losses must be accounted for. The cross-polarization correction
and coordinate transformations required are described in AppendiX C.
12
•
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NOSE
TAIL
l18-4-16993L
8=180°
(Reverse 8 scale for bottom-mounted antennas)
Fig. 6. Radiation density contours for the Lear Jet withwheels up and flaps down and antenna in bottom. front position.
13
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Thus, when some situation is defined with aircraft coordinates relative
to a ground located radar, and aircraft velocity and roll angles are known, the
first step requires that e and <p be found and the corre sponding antenna data
must then be located. The cross -polarized correction is then added to obtain
the aircraft antenna gain for that particular set of conditions.
With the aid of the coordinate conversion, cross polarization correction
and data lockup subroutines, it is a relatively simple process to obtain the
effective aircraft antenna gain under any as sumed set of conditions. It is
assumed, of course, that the aircraft antenna is well matched to the receiver
or, if not, that allowance will be made for the mismatch. Ground reflections
complicate the overall picture of the transmission channel and in the following
multipath signals are ignored in the interest of simplicity. However, any
assumed multipath model could be incorporated in the procedure with the re
suIting increased complexity and computing time.
A useful application of the data could be a plot of the conditioned proba
bility that the antenna gain will be at least as great as x dBi versus x dBi under
a set of assumed conditions. For example, if the angle of elevation of a given
aircraft is fixed at a given value, the roll angle is equally probable between
given limits and the heading is also equally probable anywhere from zero to
360°; then such a graph of the cumulation probability can be plotted and it will
have considerable value in the assessment of the relative merit of possible
antenna locations and perhaps indicate whether or not antenna diversity is
needed. Figure 7 is such a result. Further applications and reduction of
the recorded data are described in Ref. 3.
14
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NOTE:
HEADING IS EQUALLY PROBABLE FROM 0 0 TO 360 0
ROLL ANGLE IS EQUALLY PROBABLE FROM- 20 0 TO 200
1.0
0.9
0.8
>-I- 0.7...JaJ« 0.6aJ00:Q.
w 0.5>~ 0.4...J:::>~:::>u 0.3
0.2
0.1
0-40 -30 -20 -10
GAIN(dBi)
o 10 20
Fig. 7. Typical probability distribution function for antenna gain.
15
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APPENDIX A
AIRCRAFT MODELS AND ANTENNA POSITIONS
L6
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P130
..367
Fig
.A
.la
oL
ear
jet
(3/4
vie
w).
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00
P13
0-36
4
•F
ig.
A.
1b
.L
ear
jet
(to
pv
iew
)•
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P13
0-61
1
Fig
.A
.Ie
.L
ear
jet
(bo
tto
mv
iew
).
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N o
P13
0-43
3
Fig
.A
.la
.C
essn
a1
50
(3/4
vie
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APPENDIX B
PRINCIPAL PLANE PATTERNS
Figures B. 1-1 to B. 11-11 show principal plane patterns extracted
from tape data for those aircraft that were actually evaluated (aircraft
numbers 1, ,2, 4, 7, 8, 10, and 11).
50
•
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" .NOS!
tlOL 1--+-....-+--+-+-f----1f__+_+-'~_+__+_+_\-f__+_+_+_+__l•••
270.
(a) horizontal plane
110.0
•o••o•
o.o.
90.0RI.9HT WI~G
110.' I ~t--+-++4-+~!!~€~~-+-+-\~~~r++--j ...~ 0
•o•
go 0
(b) wing to wing
90.0HOS8
TH
•TA
~l-+-~""':I:;;:=t==+-++- •.•o
90.0
Fig. B. 1-1.
(c) nose to tail
lATC-47(B.l-l) LLear jet, top-mounted rear, flaps up, wheels down
51
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THBT
•
PHI :: 090.0
RIGHT WING90.NOS!
•I"Q
"OL \-+-t-+-1-t--t-+-+-1'-';:j~+-+-+-t-t-+-+~-t-l•pT
'70 90.0PHI :: t 80
(a) ho riz onta1 plane (b) wing to wing
" 0NOS!!:
PHI :: 90
110.0
•oTTo
"
1IlIiE+-+-I-I-I-;;::a:--+--I+-; 0 . 0
o.
90.0 PHI " 270
(c) nose to tailjATC-47(B.1-2) L
Fig. B. 1-2. Lear jet, top-mounted rear, flaps down, wheels down
52
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PHI = 090 0RIGHT wING
180. 0 ~ r-t-++-t-~~8iil~~~~~$;$~~~f:t--+-l-~ 0.0ffo•
90.fII0SE
teO L 1-+-+-+-4-f-+-+-+-!~jb.i-++-+--1,-+-+--+g--1•FT
270,90, U
pHI " 18(J
(a) horizontal plane (b) wing to wing
180.0
PH I :: 90
90.0PHI :: 270
(c) nose to tail
~TC-47(B.l.3) LFig. B.1-3. Lear jet, top-mounted rear, flaps up, wheels up
53
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90.NOSE:
90 0RIGHT' WINO
t80L 180 o B 0.0
• o.0
0F TT T
0W M
!NG
,no. 90.0Ph! ~ I ~ n
(a) horizontal plane (b) wing to wing
PHI : 90
90.0 PH I ~I I)
(c) nose to tail/ATC-47(B o t-4) L
Fig. B. 1-4. Lear jet, top-mounted rear, flaps down, wheels up
54
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90NOSE
ISOL 1-t-'li:-+-++--+-+---1I-+--?-~+-+-+-+---l---i-+-+{-+---1••TwINo
ino.
'.10.0RIGHT _ING
90.0
PH] :: J
PH I :: 160
(a) horizontal plane
180.0
900
(c) nose to tail
PHl :: :no
(b) wing to wing
lATC-47(Bel-5) LFig. B. 1-5. Lear jet, top-mounted front, flaps up, wheels down
55
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..
PHI ::. 090.0
RIGHT wING" .NOS8
180L o. 180.0 8 a 0
• o. 0 o., TT T
0M
27(1. 90.0 PHI ::. 180
(a) horizontal plane (b) wing to wing
90.0NOSB
PHI ::. 90
180.0
TH
•TA
~~~:t:~~--I--+---H 0.0o.
90.0 PHI ::. 210
(c) nose to tail
JATC-47(B.1-6) LFig. B. 1- 6. Lear jet top-mounted front, flaps down, wheels down
56
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PHI = 090.0RIGHT WINO
180, 0 ~ r-ttt1-j;i~~~~~~ttti:2f~t-t-ti--i'·'T ~O.
ToM
...NOSB
18' ~ t---+'~-+-t-t-+-+-+-4~~+-+-+-+-'i--+--+-l-I+--l,T
Z'10.90.0
PHJ = 180
(a) horizontal plane (b) wing fo wing
PHI = 90
no.oBoTToM
~~H~4=+:~+--!---W 0 0o.
90.0 PHI :: 270
(c) nose to tail
lATC-47(B o t-7) LFig. B. 1-7. Lear jet top-mounted front, flaps up, wheels down
57
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90N058
90.0RIGttT WING
PHI :: 0
180 L O. 180.0 B o 0
• o. 0 0P TT T
0
•
a70. 90.0PHI = 180
(a) horizontal plane (b ) wing to wing
90 0!'lOSH
PHI :: 90
180.0 ~~~~+=~--4-+-+-~0.0O.
go.oPHI :: 270
(c) nose to tail
--!ATC-47(Bel-8) l-Fig. B. 1-8. Lear jet top-mounted front, flaps down, wheels up
58
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180
L
EFT
WIN
G
90NOSE
270
(a) horizontal plane
180 r-H---t-+~*
BoTToM
90
NOSE
90
90RIGHT WING
180 r-r-I--"'lQ--rBoTToM
(b) wing to wing
TH
ET
•
TH
ET
•
(c) nose to tail
Fig. B. 1-9. Lear jet bottom-mounted rear, flaps up, wheels down
59
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•
PHI :: 090 0
RIGHT \OIIIiG
• 00 o • 0.0180L 0 o.• o. TP
TT 0
•
270. 90.0 PHI = 180
(a) horizontal plane (b) wing to wing
90 0NOSI!:
PHI:: 90
180.0 {~-W~~~~~I~+4~o.oe~ c.oTTo.
90.0
(c) nose to tail
Fig. B. 1 -10. Lear jet bottom-mounted rear, flaps down, wheels down
60
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..."OS!
90.0flIGHT WING
PI11 ::: 0
IIOL .. 111.1. ...• .. 0 .., TT T
0
•
4l70. 90.0PHI = \80
(a) horizontal plane (b) wing to wing
90.0NOS!
PHI = 90
1••.•IoTTo•
T
"•T•
"=l~+-+-+-+-+---+--i •.•·.
90.0 PHI = no
(c) nose to tail
lA'TC-47(B o l-11) I
Fig. B.l-l1. Lear jet bottom-mounted rear, flaps up, wheels up
61
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PHI '" 090.0RIGHT W1NG
110.0 Bl-j,..~:Ld;i-~~--1-~$;~~~~~2~+-++-t~ 0.0o 0TTo•
o.
"J\lOSE
1 eO L f--f--'t----t--j••T
210.90 _0
PHI " 1 fiG
(a) horizontal plane (b) wing to wing
90. CNOSE
PHI " qQ
110. 0 8Iti4<:1t?tt\1;j~~~~5t3tr-:tt10100 0oTTo•
90 ,PHI '" 270
(c) nose to tail
-~TC-47(B.1-12)LFig. B. 1 -12. Lear jet bottom-mounted rear, flaps down, wheels up
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TH
•TA
PH! : 090.0
RIGHT WINO
180L o. liD.' • 0_0• o. 00_P T
T T0
w "I
"0
•
270. 90.0 PHI : Pia
(a) horizontal plane (b) wing to wing
10 .0NOSB
PHI : ao
110.0 • rt-t-T-t~~!:=I-+-€~1EoTTo
"
=r'-r-r----t-t-t-----i 0 . 0o.
90.0PHI ': 27 a
(c) nose to tail
~TC-47(B.1-13)l_Fig. B.1-13. Lear jet bottom-mounted center, flaps up, wheels down
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..
PHI =. 09-0.0
RIGHT WING
1I0.a ~ Irr1~1\~rt:lS~~~~~~~~tt1-loD.oTo•
o.o.
'0.NOSK
•I•o
lOOL '-+--CA--+--+-+--f--if-t-+-'~+-+-+-i-t-+-+--1E:+--t•pT
270. 90.0PHT " 180
(a) horizontal plane (b) wing to wing
90. ()MOSI!:
PHI ::. 90
110. 0 t--t+-+-~;i;l~t-t-j;~~~~~~t-t+-t-+--J 0.'~ o.TTo•
90.0PHI " 270
(c) nose to tail
l\TC-47(B.1-14) LFig. B. 1-14. Lear jet bottom-mounted center, flaps down, wheels down
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PHI : n" C
RIGHT WING
180.0 ~ I-tt11-~f=:.t~~~~t:ti4~Etti~l-l0.0T I 0ToM
o.
'0.NOSE
•r•G
180~ t-t-T-t-i-t-+-+-t-i-3j~+-+-+-j-+-+-+-flLf-i
• O.T
•
270.
" 0 PHI :: ll'.C
(a) horizontal plane (b) wing to wing
90.0NOSE
PH I :: C1rl
180.0
9C 0P!11 :: no
(c) nose to tail
~TC-47(Bgl-15)~
Fig. B.1-15. Lear jet bottom-mounted center, flaps up, wheels up
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" .NOSE
90.0RIGHT WING
PHI :: 0
t 110 I.• --+-*-+-1~-t--+-+-+-1~~+-+-+-1-+-+----t----ilf-H••T
•
270" 0 PH [ :: 180
(a) horizontal plane
110.0
go.o
90.0
PHI :: 90
PH I :: 270
(b) wing to wing
(c) nose to tail
Fig. B. 1 -1 6.
~TC-47(B.1-16)LLear jet bottom-mounted center, flaps down, wheels up
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PHI ::. 090 0
RIGHT WING
180. 0 ~ 1---t-+-+-t~b~~~~~I€E3-..j::_! -~-+-Ir-+--+-1 0 • 0
TO.To"
o.
".NOSE
wI
"Q
I"~ r-ttT-j--t-j'----t_-+-+-t~tE_t_++_+_I'-+_+_~"tt_.j
• O.
T
270. 90.0 PHI=- leo
(a) horizontal plane (b) wing to wing
90.0NOSB
180.0 ::t---+-I--f-+-+--+--l 0 . 0O.
90.0PHI = Z70
(c) nose to tail
~TC-47(Bol-17)~
Fig. B.1-17. Lear jet bottom.-m.ounted front, flaps up, wheels down
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PHI = 090 0
RIGHT W!!'jG
180.0 BI-ltt1~19\t=~~rj;;~~~~Jttl0'0~ ~ o.To
"
o.o.
" .NOSS
wI
"G
,"0 L 1-+t-+-++-+-+----j-t--B*:++-+-+-I~t_+_+''rl__1•,T
270. 90.0 PHI:;. 180
(a) horizontal plane (b) wing to wing
90. I}
NOSE
PHI :;. 90
180.0 ""t-f-I-+-+-++-l 0.0o
90.0 PHI = 27()
(c) nose to tail
~TC-47(Bol-18)LFig. B.1-18. Lear jet bottom-mounted front, flaps down, wheels down
68
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90.Nasa
90 0RIOHT WINO
PHI .: 0
•
180 L t-tf++-+---1'-+--+-+-+~~+--+-+-+--j-+--+-+!H----l••T
O.
o. 180 0 ~ 1-+-++-+7'1r--F~!!f---i~~t--';:~~~f-+-++-+-l 0 . 0TO.ToM
2'10. 90.0PHI.: 1!10
(a) horizontal plane
110.0
90 0NOgS
go.O
(b) wing to wing
PHl .: 90
TH
•TA
:::t--t-I-,-+-+-t-..; 0 . 0
PHI " ,10
(c) nose to tail
Fig. B.1-19. Lear jet bottom.-m.ounted front, flaps up, wheels up
69
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90.NOSE
90 0RIGHT WINO
PHI :: 0
"
180 L O. 180.0 B 0.0
• O. 0 O.• TT T
0
"
210. 90.0 PHI : 1aD
(a) horizontal plane (b) wing to wing
90.0NOSE
PH! = 9U
180.0 ot--+-+-r--,+-+--+ 0 .0o
90.0PHI :: 210
(c) nose to tail
Fig. B. 1-20. Lear jet bottom-mounted front, flaps down, wheels up
70
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go.NOS!
"0 ~ t-t-Jf-++-+-+--lf-f--E*,+-+-+-1-f-+-+-++---lpO.
T
WI
"G
"0
o.
90.0RIGHT WING
90.0
PHr = 0
PHI '=' 180
(a) horizontal plane
90.0HOS!
PHI = 90
(b) wing to wing
180.0
•GTTo
"
~~e=t,~o.oo.
90.0 PHI =. 270
Fig. B.2-1.
(c) nose to tail
-~TC-47(B.2-1) ~
Piper Cherokee top-mounted rear, flaps up, wheels down
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PHI :: 090.0
RIGHT \oIINO
•
o. 10• •• 0.0t80L
• o. 0 o.
• TT T
0
•
270. 90. Q PHI :: I BO
(a) horizontal plane (b) wing to wing
90.0NOSB
PHI :: 90
TH
•TA
180.0 l-t-ti-t~r~~~B~~ttt":9St:ttjj0.011 I o.oTTo•
90.0 PHI :: 210
(c) nose to taillATC-47(B.2-2) L
Fig. B.2-2. Piper Cherokee top-mounted rear, flaps down, wheels down
72
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PHI = (>10.0'IUOH" WINO
t80L o. UO.O I 10.0I o. 0 o.• TT T
0
•
270. 90.0PHI = t80
(a) horizontal plane (b) wing to wing
10.0NOSI
PHI : iO
tlo.OIoTTo•
rt-::3~++-+""!!"'l~r-t-t-+-j •.•..
10.0 PHI I: 2'10
(c) nose to tail
Fig. B.2-3. Piper Cherokee top-mounted front, flaps up, wheels down
73
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00.HOSE
180 L ~-+-+~+-+-+-•PT
270.
o.o. 180.0 B
oTTo•
90.0R.IGHT WINO
90.0
PHI ::; 0
PHI ::; 180
•TA
(a) horizontal plane
180.0
90.0
PHI = 90
PHI ::; ZTO
(b) wing to wing
(c) nose to tail
Fig. B. 2-4. Piper Cherokee top-mounted front, flaps up, wheels down
74
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TH
•TA
PHI :. 090.0
RIGHT WINO
180 L O. 180.0 B 0.0
• O. 0 O.F TT T
0
•
Z70. 90.0 PHI :. 180
(a) horizontal plane (b) wing to wing
90.0Hose
PHI :: 90
180. 0 f-+-+-+-+-++-¥I~~~-+~--J:=i~bt---t:-H 0.0• O.oTTo•
90.0 PHI :: 270
(c) nose to tail--~TC-47(B.2-5) l-
Fig. B. 2-5. Piper Cherokee top-mounted front, flaps down, wheels down
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90 .NOSE'
90,O
H.IGHT WING
PHI = 0
TH
"T•
PHI = 18090.0
180.0 ~ t-t-i-·!·i--t-~~;:!:~~f'EEE:Et+ar-T---,--j0.'TO.
To
"
o.
''0
180L
"FT
(a) horizontal plane (b) wing to wing
"HI = 90
90.0PHI = 270
(c) nose to tail
-I ATC-47(B.2-6) LFig. B. 2- 6. Piper Cherokee top-mounted front, flaps up, wheels up
76
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TH
•TA
PHI:: 090.0
RIGHT WING
-i:::=r9"'-;-;'*::t-++++-+-t-I~ 0.0o.
1*.0.0 B f-I-I-foTToM
o.
270. 90.0PHI'" 180
(a) horizontal plane (b) wing to wing
90.0NOS I!':
PHr :: 90
TH
•TA
·---t-t-.j,d~-+--T---I J. 0
O.
90 0PHI ::: 270
(c) nose to tail~TC-47(B.2-7) ~
Fig. B.2-7. Piper Cherokee top-mounted front, flaps down, wheels up
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".!'lOS! " 0RIGHT WINO
PHI = 0
PHI = 1 SO90.0
,,.
180 L "' • B ...• O. 0O.P T
T T
•M
(a) horizontal plane (b) wing to wing
90.0
""OSE
PHI = 90
180.0
tiltj::m~~~ttttl°·o.
90.0PHI = 210
(c) nose to tail
Fig. B.2-8.
~ATC-47(B.2-8) ~
Piper Cherokee bottom-mounted rear, flaps up, wheels down
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90.NOSS
18. L 1-+--k++-+--+-I-t-f-';:lI!:::+-+-+-I-f-+-+::H--+--l••T
•I
•o
270 .
~(L 0RIGHT WINO
..... • 1-+-+-+-~"+-I--1I-+-+"::;;lIif-loo"oTTo•
90.0
PHI : 0
lPr-+-+--+-1'-t--l 0 .•..
PHI : 180
(a) horizontal plane
90.0Nose
PHI = 90
(b) wing to wing
teo. 0 1-+--I-...j...=+;:;~~f-+-+::~+-+..=f~frl-+-+-++--1 0 ••. ..oTTo•
90.0 PHI : 270
(c) nose to tail
Fig. B.2-9. Piper Cherokee bottom-mounted rear, flaps down, wheels down
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".!'tOSB90.0
RIGHT I;INQ
PHI = 0
TH
•TA
lO •.• • r-+-++-f3t-1-t-+--t:::'*'~""=:1::::::l~j-t-TT--t- •.•o 0T
•ow
o...wI
•o
lO.e 1-+\+++-+-t-j'-t--E~++-+-t-1!--il-+-++-lB
•T
270. 90.0 PHI = 180
(a) horizontal plane (b) wing to wing
90.0NOSE
PHI = 90
1110.0 1-+-+++--,):>--f-I-t--E*+-t-t"""""l-k-+-+++--i" O
o.
90,0PHI = 2'10
(c) nose to tail
l ATC-47(B.2-10)L
Fig. B. 2-10. Piper Cherokee bottom-mounted rear, flaps up, wheels down
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PHI :: 090.0
RIGHT WINO
"0.0 • Lt-t+i~~~r-~~~~;I:;;;j.:=Il~-if-t-+-+-i 0.001 o.TTo
"
O."OL I-'\-+-++-+-+--j-f-B~++-+-j-I-t-+-+-t--t
• o.•T
270. 90 .0 PHI ;. lilO
(a) horizontal plane (b) wing to wing
90.0NOSS
PHI :: 90
180.0 I r-t-ttj:f~~F-~~~~:±i~~~t-+-t-+-j 0.0o o.TTo
"
90.0 PHI :: 270
(c) nose to tail] ATC-47(B.2-11L
Fig. B. 2-11. Piper Cherokee bottom-mounted rear, flaps down, wheels up
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THBT
•
PHI : 090.0
RIQH't WINO
u •.• B 1-t-+-+-l:::::;:~~-~t3~+-I:::-+iIi:;-ll.-I-t-++-; •.•o O.TTo•
o.
"NOS!
wI
•G
180 L f--I-~"F-+-+-+-1f-t-+-'£-+--+-+-+-.,f-t--I-+--+---t••T
2'1'0. 90.0 PHI:;; 180
(a) horizontal plane (b) wing to wing
90.0NOS!
PHI :;; 90
UO. 0 f-+-+~=t=i~=a~t--B~±-+-+-.l~f-+-+-++-4'"B O.oTTo•
90.0 PHI :;; 270
(c) nose to tail
Fig. B. 2-12. Piper Cherokee bottom.-mounted front, flaps up, wheels down
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PHI : 0to.ORIGHT WING
180L 110.0 B ...• o. 0
O.• TT T
0
"
270. 90.0 PHI: 180
(a) horizontal plane (b) wing to wing
90.0NOS8
PHI : 90
11'.0 1-+-+-+="RIIt--f--f-I-+-::E-l--+-t--.iiliil!!'l'--I-t-+--l--;' .•. ..oTTo•
to.O PHI : 270
(c) nose to tail l ATC-47(B.2-13)L
Fig. B.2-13. Piper Cherokee bottom-mounted front, flaps down, wheels down
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90.~OS8
90.0RIGHT WINO
PHl = 0
tlOL. o. 180.0 B ...• 0
0• TT T
0
•
270. iD.OPHI = 180
(a) horizontal plane (b) wing to wing
90.0NOSI
PHI = 90
110. 0 1-+-+--f=::t~~~p.+-t~3-:-+---t---1':"h.:l-++-l--1 o.~ O.
TTo•
90.0PHI = 270
(c) nose to taill ATC-47(B.2-14)L
Fig. B.2-14. Piper Cherokee bottom-mounted front, flaps down, wheels up
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TH
•T•
PHI :I 090 .0
RIGHT WINO
2'1'0.
180L D.U'.O • 0.0I O. 0P
T o.T
TW 0
I ••0
iO.O PHI :I 180
(a) horizontal plane (b) wing to wing
90.0N0811
PHI :: 9\1
TH
•T•
lO... 1-+-+--t'~R-t-r-+-+-;:jjlE+-+-+-t-I::::iI>-+-++- •.•~ o.TTo•
90.0 PHI :: 117Q
(c) nose to tail
Fig. B.4-1. Cessna 150 top-mounted rear, flaps up, wheels down
85
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TH
•T•
PHI ::. 0'iO.O
RIGHT WING
o. UO.O 8 0.0180L0 o.• o.• TTT0
•
210. 90.0 PHI::. 180
(a) horizontal plane (b) wing to wing
110. Q
PHI ::. 90
90.0 PHI ::. 270
Fig. B. 4-2.
(c) nose to tail
Cessna 150 top-rrlOunted rear, flaps down, wheels down
86
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PHI:: 090 .0
RIGHT WING
180L o. 110.0 8 0.0
• o. 0 O.P TT T
0
•
270. 90 .0 PHI:: 180
(a) horizontal plane (b) wing to wing
90.0NOSI
PHI I: 10
11'.0
TH
•TA
~ffe(~nttm··OI \ \ O.
'0. a PHI = 211)
(c) nose to taillATC-47(Be4-3) L
Fig. B. 4- 3. Cessna 150 bottom-mounted rear, flaps up, wheels down
87
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PHJ = 090.0
RIGHT WINO...N08B
180L O. 180.08 0.0
• O. 0 O., TT T
0M
270. 90.0 PHI = 180
(a) horizontal plane (b) wing to wing
eo. I)
NonPHI = 90
110.0 I-H-f:.j.sI-++-+-~~=-~~+--I---H-+~0.'o.
90.0 PHI = 210
(c) nose to taillATC-47(Be4-4) L
Fig. B. 4-4. Cessna 150 bottom-mounted rear, flaps down, wheels down
88
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\80 L 1--t-++-+--+---1-I-+--t-:~+-+-t-iI-i-+-++-'t-l•,T
WIHQ
270.
o.
PHI
o.
90.0RIGHT WING
100 .•• 1--+-++--I::,..;j:=l-I-+-+=~:-+""1''''=•TTQ
•
90.0
PHI " 0
TH
•TA
...r-+--+-1-t-t 0 .•..
PHI" 180
(a) horizontal plane
90.0NOSS
(b) wing to wing
PHI " 10
180.0 w-+-+--~:+-+~~~~~~+_l__1_+~0.0o.
PHI " 270
(c) nose to tail
Fig. B. 4-5. Cessna 150 bottom-mounted center, flaps up, wheels down
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TH
•TA
PHI = 01110.0
RIGtlT WING
180L 180.0 B '.00 ..• o. T• TT0M
270. 90.0 PHI = t80
(a) horizontal plane (b) wing to wing
90,0MOSB
PHI :: 90
110.0 I-+-++-J~~~I-t-~~~~~~f-l-+-++-+~0.0B o.oTT0,•
1110.0 PHI = 270
(c) nose to tail
Fig. B.4-6.
lATC-47CB A 4-6) LCessna 150 bottom-mounted center, flaps down, wheels down
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Pl11 = 090.0RIGHT WINO
180.0 • t-t-+=''lt--+-+-+-f-I-t-3~++-l==1'=''lIj;::-I-+--+-+-j 0 . 0
~ 0
ToN
90 .NOS!
wING
180 ~ r-r-r++-+--t--l-t-t-:3~+-+-+-+--,I--l-+-+--Ir---j
pT
270. 90.0PHI = taO
(a) horizontal plane (b) wing to wing
90.0NOSS
110.0 'Irttt~~I~t~~~!ioTToN
PHf " to
=t-f-j'-t--t--t--i 0 . 0o.
110.0PHI = 270
(c) nose to tail~ATC-47(B.4-7) l-
Fig. B.4-7. Cessna 150 bottom-mounted front, flaps up, wheels down
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THITA
PHI ; 000.0
RIGHT wING
H-fR3~m:~dtiti···180.0 Bo O.TTo•
o.18' ~ f-J~+---j-+-+-+-t-lf--(7,~j-+-t--t-t-j-r-cfH• o.PT
270.90.0 PHI = 180
(a) horizontal plane (b) wing to wing
180.0
90.0NOSB
PHI :. 90
...--+--....j~+-~+--j• ,0.,
90.0 PHI = 270
(c) nose to tail
-!ATC-47(B.4-S) LFig. B.4-8. Cessna 150 bottom-mounted front, flaps down, wheels down
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PHI : 090. !l
RIGHT WING90 .NOS!
t80L o. tlO.O' 0.0
• o. 0 O .T
P TT 0
•
2'10. 90.0 PHI :=. t 80
(a) horizontal plane (b) wing to wing
90.0NOSE
PHI :=. 90
110 0
•oTTo•
~~~+-+-+-I--f-..,~:-t--+-I-j 0.0O.
90.0 PHf = Z10
(c) nose to tail
Fig. B.7-1.
~ATC-47(B.7-1) ~Beech Baron top-mounted rear, flaps up, wheels down
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Ptll = 090.0
RIGHT WING
180.0 8 ~+-+-+---1-~4c~~~~~t-+-""e¥~F=E=f+--+---j'·,o O.TTo•
o.
" .NOSI!:
lB,L f-+-*,-+-+-j-+-+-+-+-3JIrl-+-+-t-t-t-t--ti:-t--J. ,.•T
270. gO.O PHI = ll~n
(a) horizontal plane (b) wing to wing
90.0~OS!
PHI = 90
tlO .0
•oTTo•
~~J-+-""'~st;;:j-HH '.0o.
90.0PHI = 270
(c) nose to tail
~ATC-47(B.7-2) 1__
Fig. B.7-2. Beech Baron top-mounted rear, flaps down, wheels down
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PHI ::: 090 0
R1GHT IOrNO90 .NOSE
180 L I.' •• 0.0
• 0 o., TT T
0
•
270 90.0 PHI :: 180
(a) horizontal plane (b) wing to wing
90.0NOS!
PH! :: 90
J10. 0 LllJ~~i-.L.~~~~~+:-+-+-,-l...~f;+--l--l---1 •. •B O.oTTo•
90.0 PH! ::: 210
(c) nose to tail
Fig. B.7-3.
lATC-47 (B. 7-3) LBeech Baron top-mounted rear, flaps up, wheels down
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90 .NOS!
90 0It lGHT WI NG
PHI = 0
l8OL~+-II---I--I-f-+-+--1--f~~+-++-t--,f-+-+---Hrl-1•,T
WI
•o
o.180. 0 ~ f-+-+-+-I-i-~=I.IIJ\7J~r--+--t--tIrc:t::F-r-tI:.· 0
TTo•
270. go.OPHI = 160
(a) ho riz ontal plane
90.0NOSE
PHI : 90
(b) wing to wing
no.o•oTTo•
TH
•TA
':::::l~~+-+-+-\-I-::e:±--+-\--l 0 . 0o
90.0PHI = 270
(c) nose to tail--IATC-47(B.7-4) 1__
Fig. B.7-4. Beech Baron top-mounted rear, flaps down, wheels up
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PHI ::: 1"0
PHI '= 090.0
RIGHT wpm
qo.o
"'-8+;:.-l-+-+--=+=1-t,.--t--+--+--j· .•II•.•• I-+-+-+--+--+--i==oTTo•W
INo
,.." I-t-t-++-+-+••T
(a) horizontal plane (b) wing to wing
90.0NOSE
P"'I ::: qO
uo.o•oTToN
q='I-+-",,=:;;;;;;.+-!-H 0 .•
o
110.0 PI11 ::: ~? II
(c) nose to tail
Fig. B. 7 -5. Beech Baron top-mounted front, flaps up, wheels down
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180 L f-t--&--+-+-+-+••T
w,•o
1".0 I f-f-+-+-+-+--:boTTo•
'Ml " 0
~~Pl~-l---+--+-~:"'-~"--l---+-...j •.•o.
210. 90.0PHI : ''til
(a) horizontal plane
10.0N08!
'MI : ~o
(b) wing to wing
",;, 'Ittti1-j:=~~~~7=9i~;!!l~fftt-t--i°"oTTo•
.. ,p~, : ~'n
(c) nose to tail
~ATC-47(Bo7-6) ~
Fig. B.7-6. Beech Baron top-mounted front, flaps down, wheels down
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...NO~!
1I0L I--+--\-~+-+-+••T•J
•G
210
"0.0~ r-t-t-t-+-+--t;iiJ!:TTo•
90.0AIOH" WffolG
PHI ': 0
(a) horizontal plane
' •. 0MOSI
PH' : 'iIQ
(b) wing to wing
"I.' I-ttttti2:ii~cJjt'~~S5Efttttl0·0It ".GTTG
•
110.0
(c) nose to tail
~ATC-47(Bo7-7) 1__
Fig. B.7-7. Beech Baron top-mounted front, flaps up, wheels up
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PH! = 090.0RfGHT WINO
110.0 • r-~+-+-+--+::;;-=~-f--'4-+-j---==1P""'''''''+-+--+--j 0 • 0oTTo•W
I
•Q
...L r-r--ft-+-+--t--j••T
l'lC90 _0 '"I
(a) horizontal plane (b) wing to wing
90 .01r40SB
PHI '" IlO
180.0 t-t-+-+-++-±:5C±~?+8~;;;lt=~F~+--:-+---I0.0o.
90,0 PHt ,. ~7 ()
(c) nose to tail~ATC-47(B.7-8) l-
Fig. B. 7 -8. Beech Baron top-mounted front, flaps down, wheels up
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90.NOSS
90.0RIGHT WINO
PHI :: 0
PHI :: 15090.0
110. 0 ~ 1-t--t-+-t~>t-lI-t-t~:r-:::::f~~Ft-t-+T---t--l 00.- 0
TTo•
').
•J
•o
II." t-t-+-++-+-+-I,-t-~~+-+-+"""':-!-~-'-+-i--l•pT
(a) horizontal plane (b) wing to wing
90.0NOS"!
P!il ::. 9C
uo. 0 1--+-++-h.a=:::l-f-.j-+,;JE+-l''''1=~.j-+-+-+--+-+ •. 0
~ o.TTo•
90.0PHI :: 270
(c) nose to tailIATC-47(Bo 7-9)L
Fig. B.7-9. Beech Baron bottom-mounted rear, flaps up, wheels down
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".NOsa90.O
RIGHT WIlIlG
PHI = 0
180L f-t{t-++-+-+-j-f-8~++-t-i--j'-P''k++--1• O.•T
110.0 B I-+-++-+;;---i-I-+---+::~=+O!!!'''''''edb-I-+-+-+-+-il 0 . 0
~ O.
To•
2'IQ .90.0
PHI = 180
(a) horizontal plane
90.0NOSI!:
PI'H =. 90
(b) wing to wing
180.0 f-+-++--'(;d:=-1-f-+--P~4--t.....j.....lej!!::+-++-t--10.0
90.0 PHI =. 270
(c) nose to tail
~ATC-47(B.7-10)~
Fig. B. 7-10. Beech Baron bottom-mounted rear, flaps down, wheels down
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TH
•T•
PHI = 090.0RIGHT WING
180L 180.0. 0 .•
• .. • ·.• f~f ••
210. 90.0P.HI = 180
(a) horizontal plane (b) wing to wing
90.0NOSB
PHI = 90
110.0 8I-ttttl''tsiFt~~~~:i'li~~ttttl.. 001 o.TT
••
90.0 PHI = 2'10
(c) nose to tailIATC..47 (B. 7-11)L
..Fig. B.7-11 . Beech Baron bottom-mounted rear, flaps up, wheels up
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"NOSI!:
90.0RIGHT WING
PHI :: 0
180 L 1110.0 B 0.0
• o. 0 o.• TT T
0
•
2'0" 0 PHI : 180
(a) horizontal plane (b) wing to wing
90.0NOSI!:
PHI = 90
180.0
Htt~ttW~f?Hrtt1°·0o.
90.0PHI :: 270
(c) nose to taillATC-47(Bo 7-12) L
Fig. B. 7 -12. Beech Baron bottom-mounted rear, flaps down, wheels up
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PHI -= 090,0
RIGHT WING".NOSB
180L 110.0 B ...• 0 o.P TT T
0W "I
"0
210.90.0 PHI :: 180
(a) horizontal plane (b) wing to wing
180.0
PHI -= 90
90.0 PHI = 270
(c) nose to tailjATC-47(B.7-13)~
..Fig. B.7-13• Beech Baron bottom-mounted front, flaps down, wheels down
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9 •.NOSE
90.0RIGHT WINO
PHI ,. 0
180L o. 180.0 III 0.0B
O.0 ..
P TT T
0
•
2'70. go.oPHI ,. 180
(a) horizontal plane (b) wing to wing
90.0NOSE
Ptl r ,. 90
180.' 1--l--J-___1_~q~=~~?:::~:+_+.......a~f_+_+____1___+____l 0 . 0
• o.oTTo•
90.0 PHI ,. Z10
(c) nose to tail~ATC-47(B.7-14)~
Fig. B. 7 -14. Beech Baron bottom-mounted front, flaps up, wheels up
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PHI = 090.0
RIGHT WING
180L o. 180.0 B ...• o. 0 ..• TT T
0
"
a'l'o. 90.0 PHI = 180
(a) horizontal plane (b) wing to wing
90.0NOSS
PHI = to
110.'IoTTo
"
T
•IT
•
d=~+-+-t--+--+-1 •.•o.
00.0 PHI = 2'1'0
(c) nose to tail
Fig. B. 7 -15. Beech Baron bottom-mounted front, flaps down, wheels up
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TH
•T•
PHI :: 0
q..+~~F~hH-j •.•O.
90.0RIGHT WING
180 .0 B I--l--+--+--+--+-f-f'"o•To•
o.
•I•o
11. L 1--H~+-+--+----t---1f-f--R~+-l--+--t~f-t-+-f-lIt--i• o.p
•
270. 90.0 PHI :: 1 flO
(a) horizontal plane (b) wing to wing
90.0HOSH
PHI :: 90
180.0
•oT
•o•
::-+---1--... =-1'-+--1---1,--1--1 •.•O.
90.0 PHI :: 270
(c) nose to tail
Fig. B.8-1.
l ATC-47(B.8-1) [_
Beech B-99 top-mounted rear, flaps up, wheels down
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PHI:: 0
PHI:: 180
~-+-t--::l5lF-1-t-t-t-I0.00,
90.0RIGHT WINO
go .0
"I. I • I--i-+-++-+-t-lr:o~
~
o•
,HI
O.\80L 1--H4-++-+-4-j~t-BIE++-+-t:I-t-t--t1rt-"i• 0,PT
(a) horizontal plane (b) wing to wing
to .0NOSI
'HI • so
110.0
•oTTo
"
TH
•T•
U.O PHI :: 2'1'0
(c) nose to tail
Fig. B. 8-2.
-J ATC-47(B o 8-2) 1_Beech B-99 top-mounted rear, flaps down, wheels down
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PHI = 090.0
fliGHT WING
110. 0 ~ Ittti1~;;rt~m;;t:t~9;;:t:t.:tt11 0°.0
TTo•
180 L 1-t++-++-+---+-1~!-+':::~++-+--+-1f-t-+--t-Ir-t---l•,T
270. 90.0 PHI : 180
(a) horizontal plane (b) wing to wing
90.0NOS!
PHI = 90
90. (] PHI = 270
(c) nose to tail l ATC-47(B.8-3) 1_Fig. B.8-3. Beech B-99 top-mounted front, flaps down, wheels down
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PHI = 0" 0
liGHT WINO
180.0 B f.-t-t-tti-l~!!!!!~~~1::t~~~~ttttl'·'o l o.TTo•
o...
" .NOSI
WI
•o
180 L 1--hH-+-+-+--j-f-+--+-,3lIIf-+--+-1-.,f-t-+--+--H-+-1•pT
a'l'o. 90.0 PHI = 180
(a) horizontal plane (b) wing to wing
90.0M0811
PHI : '0
110.0
•oTTo•
TH
•T•
H--j-jiiiiI!!j;;;;;±-+-t-t-ti • .•·.
tlo. QPHI = Z70
(c) nose to tail l ATC-47(B.8-4) 1_Fig. B.8-4. Beech B-99 top-mounted front, flaps up, wheels up
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90N,,)SE
90 0RYGIoiT "'IlIIG
PHI :- 0
180L 180.0 B 0.0• 0 O.P TT T
0w "I
"0
270.90.0 PHI = 180
(a) horizontal plane (b) wing to wing
90.0
!'lOS!
'HI :- 90
180.0 I-+-+-++++..,f~~1lIE+++....=:J--+-+-t-H 0 0c
90 0 PHI :: 270
(c) nose to tail l ATC-47(B.8-5) LFig. B.8-5. Beech B-99 top-mounted front, flaps down, wheels up
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"NOS!qO 0
RTO>1T IOINO
PHI " 0
PHI = 18090,0'"
180L O. II• •• 0.0• • 0,T
T T0
W •I
•Q
(a) horizontal plane (b) wing to wing
" 0!'Ie::;!
PHI : 90
180.0 8Itt11~rtt1;dlt~ii!:1~~/:tt1j-0 0oTTo•
go.OPHI " Z10
•
(c) nose to tail
-I ATC-47(B.8-6) LFig. B.8-6. Beech B-99 bottom-mounted rear, flaps up, wheels down
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90 .NOSE
90.0RIGHT WING
PHI : 0
180 L f--I-+ld---+-+--t--"f--+-+-:;~+-+-+--t-t-+--H'-j--t---j•pT
180.0 BLt-t-f~~:f~~t~~~~~9~~bt-ttl 0.001 o.TTo•
ll'lO. 90.0 PHI = 180
(a) horizontal plane
110.'
90,0NOS8
90.0
(b) wing to wing
PHl = 90
:Iii;:;;t---+-+---t-r-r- 0.0o
PHI = 2'10
(c) nose to tail
l ATC-47<B.8-7) 1_Fig. B.8-7. Beech B-99 bottom-mounted rear, flaps down, wheels down
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90 .NOSB
90.0RIGHT WING
PHI = 0
t80L o. 180.0 B 0.0
• O. 0 O.• TT T
0
•
Z70. 90.0 PH[ = 180
(a) horizontal plane (b) wing to wing
90.0NOSH
PHI : 90
180.0
•oTT_o•
'!!I;;.-+--,I-+---+---+--t---1 0 . 0o.
90.0 PHI = Z70
(c) nose to tailI ATC-47(B.8-8) L
Fig. B.8-8. Beech B-99 bottom-mounted rear, flaps up, wheels up
115
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" .NOS!90.0
RIGHT WINO
PH[ ::: 0
180 L 1-+-~+-+-+--f-f-+-+:~+-+-t-l-t-+--r."I--+--I•pT
wI
•Q
o.o.
1110.0 II ri-l~~~t~ij2~~~=Ltiid~~H 0.0o o.TTo•
210 90.0PHI = 180
(a) horizontal plane
90.0HOS!
'PHI = 90
(b) wing to wing
180.0 0 0
• o.0TTQ
•
90.0 PHI = 2:'10
(c) nose to taillATC-47(B.a-9) L
Fig. B.8-9. Beech B-99 bottom-mounted rear, flaps down, wheels up
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'.1'0'.8 " 0RIGHT WHIG
PHI :: 0
180L O. 180.0 B 0,08
O.0 0,• T
T T0
•
270. QO.OPHI:: t80
(a) horizontal plane (b) wing to wing
90.0MOSI
'HI = to
TH8TA
180. 0 1-+-+--F~...t-!~I-+--EllItoiid--jo~~="t-t--r-T-t1 0,0• 0,oTTo•
00.0 PHI = 2'10
•
(c) nose to tail l ATC-47(B.a-lO)I_
Fig. B.8-l0. Beech B-99 bottom-mounted center, flaps down, wheels down
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PHI =- 090.0RIGHT WINO
90 .NOSB
teOL o. 110.0 I 0.0• o. 0, 0TT T
0M
~7 0 .go.O
PHI = 180
(a) horizontal plane (b) wing to wing
90.0NOS8
PHI : 90
180.0HTtl~\t3<1~~t:tt110.0o.
90.0 PHI = Z70
(c) nose to tail l ATC-47(B.S-ll)L
Fig. B. 8 -11. Beech B-99 bottom-mounted center, flaps up, wheels up
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PHI = 090.0RIGHT WINO
110. 0 ~ r-rt\::f:t;J~?~~~~~~~1~1+---+-+-+-+-J: .. 0
To
"
...NOSI
•I
"o
110 ~ t-t-+;;:ji;;;p-t---t--,I--t-+:~+-+-+--i-t-+-OE£"++-1o. o.PT
270.'0.0 PHI = 180
(a) horizontal plane (b) wing to wing
10 .0",>a.PHI :I '0
110.0
•oTTo
"
TH
•T•
:-I-Ioo:;i:",+-++-+-+--i 0.0o.
to.O PHI = 2'10
(c) nose to taillATC-47(B.8~12)~
Fig. B. 8-12. Beech B-99 bottom-mounted center, flaps down, wheels up
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90.NOS8
• 90.0RIGHT WINO
PHI = 0
180 L I--+--t-li+-+-+-j-r-+-+:;~+-+-+-j-r-+-+t,>j---t-j
• o.PT
o. 110.0 B~+-+-+~;!,..t-iLI-B~~~=+~~~b+-++-1 0.0~ 0To•
210. 90.0PHI ; 180
(a) horizontal plane
90.0HOSB
PHI = 90
(b) wing to wing
180.0 H-tWPrn~st-m.+1°·oo.
90.0PHI = 210
(c) nose to tail
l ATC-47(Be8-13)L
Fig. B.8-13. Beech B-99 bottom-mounted front, flaps down, wheels down
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PHI :: I!)O
PHI :: 0
90.0
" 0IUGHT WltiO
180L o. taO.O '8 0.0
• o. 0P TT T
0•
(a) horizontal plane (b) wing to wing
90.0NOSE
PHI :: 90
180.0 Br-ttt~11~rt~it~~~l:lt~ttttl 0°.0
oTTo•
90.0 PH! :: 27 C
(c) nose to tailIATC-47(B.8-14)~
Fig. B.8-14. Beech B-99 bottom-mounted front, flaps up, wheels up
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".MOSE!:90.0
RIGHT WIHG
PHI : 0
180L I-+-+-Jl-+-+---+-II-t-+::~+-+-+--j-I-+-+:»-+--l•pT
wING
180.0 B 1-+-+-~4",*d;:;-I-+--t-:::~+-+~~et=:+-+--+--+-1 0 . 0
~ O.
To
"
2'10. 90 0PHI " 180
(a) horizontal plane
90.0HOSE
PHI " 90
(b) wing to wing
110.0 8 ~t-+i4~~~f-f-:~~~si~~t-~t-+i-+-1 0.0o O.
TToN
90.0PHI " ,70
(c) nose to taillATC-47(B.8-15)L
Fig. B.8-15. Beech B-99 bottom-mounted front, flaps down, wheels up
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90 .NOSI!
90.ORIGHT WINO
PHI = 0
1eo L o. 180.08 0.0B o. 0 o., TT T
0
•
270. gO _0PHI: 180
(a) horizontal plane (b) wing to wing
90.0HOS!
PHI ; 90
THBT
•
110. 0 1-+--+-~;;~33i="f~:t-~:;i ~!!F+-+--t-l~H 0.0B o.oTTo•
90.0 PHI = 270
(c) nose to tail~ATC-47(B.l0-l)l-
Fig. B. 10-1. Helio u-Io/n bottom-mounted rear, flaps up, wheels down
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TH
•TA
PHI = 090.0RIGHT WINO
180. 0 ~ t-t-+-++-t--:::I~~+-~~~"'.;.,.j.--I-1-+-++--1 0.0
TO.
ToM
o.O.
90.NOSB
WIMQ
180 L I-+-J't-+-+--+--+-I-t-+-;~+-+--t--t-f-t-t•pT
270.90.0
PHI = 180
(a) horizontal plane (b) wing to wing
90.0NOSB
PHI = 90
110.0 1-t--I-+'::t:~~-j-I-+:3~+.,.i::t::=t~r-t-+-+-+-i0.0o.
90.0 PHI = 270
(c) nose to taillATC-47(B e l0-2) L
Fig. B.10-2. Helio U-IO/n bottom':'mounted rear, flaps down, wheels down
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PH) :: 0
~l...~;:;;O+-+--+-1-H •.•..
90.0RIOHT WINO
180. 0 ~ 1-f-'+-+:f~~;=s~~-8lTTo•
..
'0.NOSI
wI
"Q
'" L f--f-'!>}-++-+-f--..,f--f-+:;IE+-+-f-jf--+-+-+-+rI--1. ..,T
270.90.0 PHI :: 180
(a) horizontal plane (b) wing to wing
iQ. "NOSB
PHI :: 90
180.0 l-t-tt=f4~4Fr:~~~~id~~t-t-ttl.·.go.TTo•
90.0 PHI :: 270
(c) nose to tail
~ATC-47(B.I0-3)l-
Fig. B.10-3. Helio U-10/n bottom-mounted front, flaps up, wheels down
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PHI = 090.0
RIGHT WING
180L o. 180.0 B 0.0 •• 0 o.• TT T
0W •INQ
270. 90.0 PHl = 1 BO
(a) horizontal plane (b) wing to wing
90.0NOS!
PHI = 90
180.0 iiiO:;r:-r-+-+-t----t-t- 0.0
90.0 PHI = 270
(c) nose to taillATC-47(B.I0-4) L
Fig. B. 10-4. Helio U -1 DID bottom-mounted front, flaps down, wheels down
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".NOSE90.0
RIGHT WING
PHI = 0
180 L O. 180.0 B• O. 0 O.F TT T
0
"
270. 90.0PHI = 180
(a) horizontal plane (b) wing to wing
90.0NOS!
PHI : 90
180.0
TH
•TA
g-o.oPHI = no
(c) nose to tail
Fig. B.11-1. Grumman Gul£stream top-mounted rear, flaps up, wheels down
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90 .NOSP'
180 L f--H+-+ -+-+-+--+--1- -L"'i::---;-+-~---t---+-c-t-c.)---;-----+
•FT
Z'IO.
o.
180. a 8oTTo
"
150.0
90 0RIGHT WING
90.0
PHI: 0
PHI =: 180
TH
•TA
(a) horizontal plane
90 0NOSE
PHI = 90
(b) wing to wing
180 .0
•oTTo
"
TH
•TA
";~~:j -j----,H-<~_+--+--,----j 0.0o.
90.0 PHI = Z'IO
(c) nose to taillATC-47(BeU-2) L
Fig. B. 11- 2. Grumman Gulfstream top-mounted rear, flaps down, wheels down
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90.NOSE
90.0RIGHT WINO
PHl ;: 0
I SOL O. 180.0 8 0.0
• 0O.
F TT T
0
•
270. 90.0PHl '" 160
(a) horizontal plane (b) wing to wing
ao.oHOSE
PHI = 90
TH
•TA
180. 0 r-r-FFFFF\:5~~tE;t+-+-+-+';F+-+-+-+-10.0~ O.
TTo•
80.0 PHI = Z70
(e) nose to tail~ATC-47(B.11-3)~
Fig. B. 11- 3. Grumman Gulfstream top-mounted rear, flaps down, wheels up
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PH! = 090.0RfGHT wiNG
180.0 B f--1-+-++-+--+'!!!!iIl::~~*,+-t---t----.j~Io---l-+--+--+---1 0.0oT o.TG
•
o .
wING
180 L I-MIt--+-++--t-t••T
27090.0
PHI = 1 tiO
(a) horizontal plane (b) wing to wing
180.0
•oTTo•
'til = ge
~+-+-+==l==+'''''+-+---l----;i------I0 . 0o
9(10P I-t [ : ? 1 ~)
(c) nose to taillATC-47 (B e ll-4) L
Fig. B. 11-4. Grumman Gulfstream top-mounted front, flaps up. wheels down
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PH I = 090.0"'(GMT wINO"NOS!
noL 110.0 B 0.0• O. 0• T 0T T
0
•
210.90.0
PI1' = I ~ r:
(a) horizontal plane (b) wing to wing
90.0NOSS
PH! : 90
,eo.o t-t-+--+--+-+-+-'" i!l:;;;+~~-1-F:j:::+"~,.-+-+-+--l0 . 0
~ O.
TTo•
90'.0fit-! r : 270
(c) nose to taillATC-47(B.11-S) 1_
Fig. B. 11- 5. Grumman Gulfstream top-mounted front, flaps up, wheels up
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PHI =: 090.0
~JGHT WINO
t80LI o. 180.0 B 0.0
• 0 0 O .• TT T
0
•
2'Ul90.0 PHI =: 1900
(a) horizontal plane (b) wing to wing
90 0NOSE
PH I = 90
180.0 r-~HHH--+~==i~::~4--\.-:\==t::::r",J-++--+------J0.0o.
90 0PHI = ?7C
(c) nose to taill\TC-47(B.1l-6) L
Fig. B. 11-6. Grumman Gulfstream top-mounted front, flaps down, wheels up
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PH I = 090.0
RIGHT WINO
180L o. 110.' • 0.0
• o. 0 o.• TT T
0
•
...
Z7C 90.0PHI = 1 \'10
(a) horizontal plane (b) wing to wing
90 0NOSlI'
PHI = 90
110.0
•oTTo•
~Ft--t--t---t--t-t----j •.•/'.£4JW"'....N •.
90 0 PHI : no
)
(c) nose to tail
Fig. B. 11-7. Grumman Gulfstream bottom-mounted rear, flaps up, wheels down
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90.NOSE
90.0RIGHT WING
PH I :: 0
lOa" /-+-y"9--+-t--1l-f--+-+~~-+--1I-l-+-+--l'-d--+1-•,T
WINo
a.a .
110. 0 ~ Ittt1:if===1It-t~~~~il~tt:ttii--j a. aT a.ToN
Z70." a PH ( :: I ~o
(a) horizontal plane
110.0
•oTTo•
90.0NOS!
" 0
(b) wing to wing
PHI :: 90
"'''-I--f-l-l-+-+---1 a. aa.
PH I :: 270
(c) nose to tail-~TC-47(B.11-8)L
Fig. B. 11-8. Grumman Gulfstream bottom-mounted rear, flaps down, wheels down
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,Hl =- 090. Q
11Q"1 ",PlIO
..'" 110.0 • 0.0
• 0 O•
• O. ,, ,0
•
110. to.D PHI :t tlO
(a) horizontal plane (b) wing to wing
.....•o,,o•
'"1 :: to
T
"•,•
fIIaI-I--I--I-l-lH •.•t.
1•. 0 'HI. no
(c ) no s e to tailliWC-47(B.1l-9)L
Fig. B. 11-9. Grumman Gul£stream bottom-mounted rear, flaps up, wheels up
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TH
•T•
PHI :: C90.0RIGHT WI!'iG
HO.D ~ l-t-tt~11-t-t~~~ji~:-~tti:i--jO.0Tl o.To
"
O.
" ."to!'!E
•I
"o
180 ~ r-t-if+-t-+--t---,f-t-+;:~+-+-+-I-I--l-.fl>+-+-lpO.
T
210 .90.0
PH I :: I ~o
(a) horizontal plane (b) wing to wing
90.0!"OS!!:
PHI :; gO
110.08oTTo
"
~I'-+-+--+--+--+-+--l 0 . 0o.
PHI :: :il70
(c) nose to tail
Fig. B. 11-10. Grumman Gul£stream bottom-mounted rear, flaps down, wheels up
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•H TI H
•T1.1' •
...
,..\;. I. 110.1 • 1.1• I. 0P. or I.
or or0.. •I••
... 10.0 PHI • 110
(a) horizontal plane (b) wing to wing
10.010••
,....IoTTo•
T••T•
Mo-+-++++.....o.
.... 'HI • I"
(c) nose to tail---roTC-47 (B 011-11)L
Fig. B. 11 -11. Grumman Gulfstream bottom-mounted front, flaps up, wheels up
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APPENDIX C
CROSS-POLARIZATION LOSS AND COORDINATE CONVERSION
Figure 4 shows the model aircraft and tower geometry. The polariza-
tion vector lies in the plane defined by the yaw axis of the model aircraft and
the line joining the transmitter to the model aircraft. This happens to be the
horizontal plane in this case and this condition is maintained throughout the
whole measurement process. When an aircraft in flight receives radiation
from a vertically polarized antenna on the ground, there is correspondence
to the experimental setup as long as the aircraft is in straight and level flight.
However, any change in flying conditions involving rolling, climbing, or diving
will result in the polarization vector flying outside of the above mentioned
plane.
In vector notation the polarization vector p can be expressed as follows:.... .
Let i be a unit vector in the axis of the transmittingz
dipole elements of a ground antenna
and pbe a unit vector in the line joining the origin of
coordinates in the aircraft to the point of observation,
i. e., the transmitting antenna on the ground
(1 x-p~- z _
then p = x p[( x PIz
where x signifies vector cross product.
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-Let i be a unit vector defining the yaw axis of the aircraft (and the air-yaw
craft antenna) and let N be a unit vector normal to the plane defined by pand-i yaw
then -N=
The fraction of the incident signal voltage which is sensed by the aircraft- -antenna is IN x r I, a quantity always less than or equal to unity. The other
component of p is cross -polarized and contributes nothing to the received sig-
nal. Therefore, in practical situations involving aircraft maneuvers, 20 loglO
INx 'PI should be added to the measured antenna directivity. This is one of
the quantities computed in a subroutine which also obtains the required co-
ordinate transformations described below.
Let XI' YI' 2 r be the target aircraft coordinates with respect to the
ground antenna. The positive directions of the corresponding axes are East,
- - -North and vertically up, respectively, and i , i , i are unit vectors on thesex y z
axes. Target information expressed in any other form can always be trans-
formed to fit the description.
Let £. m and n be direction cosines defining the unit vector on the
aircraft velocity vector, thus defining the aircraft heading in the horizontal
plane and the pitch angle. Heading will be defined as the clockwise angle
measured from North to the velocity vector and pitch is measured from the
horizontal plane to the velocity vector. It is positive if up and negative if
down.
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Let R be the roll angle of the aircraft. This is zero in straight and
level flight and is regarded as positive if the aircraft is rotated clockwise as
seen from the tail.
The coordinates of the aircraft relative to the ground antenna define
- -both p and p
- 1P =r=======-, Ix 2+ y 2 + Z 2V· I I I
{ -X i -I x
-YI \ - Z i}I z
(i:x p)Ii x;\z
1=" 1v-2 + y 2~I I
The velocity vector roll angle defines the roll, pitch and yaw axes of
the aircraft
i is a unit vector on the yaw axis of the aircraft.yaw-iroll is a unit vector on the roll axis of the aircraft •..-. -. ~ .......
:. i 11 = 1 i + m i + n i .ro x y z
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-Since the roll axis coincides with the velocity vector. i 't h is a unit vectorpI c
on the pitch axis of the aircraft. When the roll angle is zero
and when the roll angle can have any value
i h = ---;===1==:::::;- rem cos R - nisin R) i x -(1 cos R + nm sin R) iypitc ,I 2 2 L
Vm + R.
t cos R + m sin R) i - (nm cos R- 1. sin R) ix y
)
2 2 -]+ (I + m ) cos R i z
The necessary steps to obtain the correction for cross polarization are now
obvious. Because of the cumbersome expressions involved, the results of the
vector eros s products will not be written in expanded form; but it is a simple
computer operation and needs no further description.
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The aircraft coordinate angles e and ¢ are now very simply obtained
as follows:
- -cos e· =i . pyaw
-I{- -}• e = cos i . pyaw
tan ¢ = (p. t;itchj- 7P • Iroll
- -¢ = tan-II ~.. ~itCh j
Prall
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{1.
BIB LIOG RA PHY
"Technical Development Plan for a Discrete Address Beacon System, II
Report No. FAA-RD-71-79, October 1974 Final Report, IV -29, IV -30,IV - 31, Department of Transportation, Federal Aviation Administration,Washington, D. C. 20590
2. Ibid., V -13.
3. Schlieckert, G. J., "An Analysis of Aircraft L-Band Beacon AntennaPatterns, " M. I. T. Lincoln Laboratory, FAA-RD-74-144 (15 January1975).
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