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ILA-36 Orlando, FL October 2007
Avionics Engineering
Center
Computer Modeling of Loran-C Additional Secondary Factors
Janet Blazyk, MSDavid Diggle, PhDAvionics Engineering CenterOhio University, Athens, OH
ILA-36 Orlando, FL October 2007Avionics
Engineering Center
2
BALOR Computer Program
Models Loran-C propagation over ground. Computes field strength, ASF, and ECD. Considers terrain elevation and ground
conductivity. Developed by Paul Williams and David Last,
University of Wales, Bangor, UK. The name “BALOR” comes from BAngor
LORan. The Avionics Engineering Center at Ohio
University took over maintenance of the BALOR software in March 2005.
ILA-36 Orlando, FL October 2007Avionics
Engineering Center
3
Factors Affecting Loran-C Propagation Primary Factor (PF) – accounts for the speed of
propagation through the atmosphere, rather than through a vacuum.
Secondary Factor (SF) – accounts for the time difference for a signal traveling over a spherical seawater surface, rather than through the atmosphere.
Additional Secondary Factor (ASF) – accounts for the time difference for a signal path that is at least partly over terrain, rather than all seawater, as well as any other factors that may come into play.
ASFs are affected by Ground conductivity Changes in terrain elevation Receiver elevation Temporal changes (seasons, time-of-day, local weather)
ILA-36 Orlando, FL October 2007Avionics
Engineering Center
4
US Ground Conductivity Map
“M3 map” from CFR Radio and Television Rules (47 CFR 73.170)
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Engineering Center
5
0
4
8
12
16
20
24
28
32
0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
Distance from Transmitter (km)
Ph
ase
Lag
(m
icro
seco
nd
s)
seawater = Loran secondary factor
Phase of attenuation in relation to conductivity
ILA-36 Orlando, FL October 2007Avionics
Engineering Center
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Additional secondary factor in relation to conductivity
0
4
8
12
16
20
24
0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
Distance from Transmitter (km)
AS
F (
mic
rose
con
ds)
ILA-36 Orlando, FL October 2007Avionics
Engineering Center
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Sample BALOR plot of predicted ASFs
BALOR predicts ASFs that are corrections to single-station TOA values.
The transmitter here is Carolina Beach.
Note how ASF values are very low over the ocean, but generally higher and more variable over land.
ILA-36 Orlando, FL October 2007Avionics
Engineering Center
8
Effective earth radius
Except at very low frequency, radio waves are refracted by the atmosphere to some extent.
If we assume a linear vertical lapse rate, then this effect may be modeled by multiplying the actual earth radius by some factor, which we will call the effective earth radius factor (eerf).
The traditional value for the eerf is 4/3, but the value should probably be smaller for lower frequencies such as the Loran frequency.
(The inverse, the vertical lapse rate, is also commonly used. In this case, the traditional value is clearly 0.75.)
ILA-36 Orlando, FL October 2007Avionics
Engineering Center
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Effective Earth Radius Factor
From S. Rotheram, IEE Proc., Vol. 128, Pt. F, No. 5, October 1981
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Engineering Center
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Effect of effective earth radius on phase delay
0
5
10
15
20
25
30
35
0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
Distance from Transmitter (km)
Ph
ase D
ela
y (
mic
roseco
nd
s)
flat and sandy soil or rocky and steep hills
average soil
seawater
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Engineering Center
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Height Gain Factor This factor comes into play in two ways:
First, it is part of the solution for irregular terrain – if a point is on a hill, it is as if it were a raised transmitter or receiver.
Second, if we are actually modeling an elevated receiver, say in an aircraft, then we need to apply the height gain factor again to the ground-based solution.
The height gain factor is a complex function of height, distance, and ground conductivity.
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Engineering Center
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Relative magnitude of attenuation vs. receiver heightae=1.14a, sigma=5S/m, epsilon=80
0.95
1.00
1.05
1.10
1.15
1.20
1.25
1.30
1.35
1.40
1.45
0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000
Receiver Elevation (m)
Mag
nit
ud
e R
ela
tive t
o E
levati
on
= 0
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Engineering Center
13
Phase offset vs. receiver heightae=1.14a, sigma=5S/m, epsilon=80
-1
0
1
2
3
4
5
6
7
8
9
0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000
Receiver Elevation (m)
Ph
ase O
ffset
(rad
ian
s)
Rela
tive t
o E
levati
on
= 0
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Engineering Center
14
Relative magnitude of attenuation vs. receiver heightae=1.14a, sigma=0.001S/m, epsilon=15
0.70
0.80
0.90
1.00
1.10
1.20
1.30
1.40
1.50
1.60
1.70
0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000
Receiver Elevation (m)
Mag
nit
ud
e R
ela
tive t
o E
levati
on
= 0
ILA-36 Orlando, FL October 2007Avionics
Engineering Center
15
Phase offset vs. receiver heightae=1.14a, sigma=0.001S/m, epsilon=15
-1
0
1
2
3
4
5
6
7
8
9
0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000
Receiver Elevation (m)
Ph
ase O
ffset
(rad
ian
s)
Rela
tive t
o E
levati
on
= 0
ILA-36 Orlando, FL October 2007
Avionics Engineering
Center
“Worst Case Path” Examples
ILA-36 Orlando, FL October 2007Avionics
Engineering Center
17
“Worst Case Path”
In their 1979 report, Burt Gambill and Kenneth Schwartz described a path along the radial from the Loran transmitter at Searchlight to Fort Cronkhite, near San Francisco Bay.
Because of the extremes in terrain along the path, they called it the “Worst Case Path”, or WCP.
It makes a nice example, so we will make use of this path as well.
Searchlight
Fort Cronkhite
124 W 122
W 120
W 118
W 116
W 114
W
34 N
36 N
38 N
40 N
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Engineering Center
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Terrain Elevation over “Worst Case Path”
-500
0
500
1000
1500
2000
2500
3000
3500
4000
4500
0 100 200 300 400 500 600 700 800
Distance from Transmitter (km)
Te
rra
in E
lev
ati
on
(m
)
Death Valley
Mount Langley
Searchlight
Fort Cronkhite
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Engineering Center
19
Ground Conductivity over “Worst Case Path”
0.001
0.01
0.1
1
10
0 100 200 300 400 500 600 700 800
Distance from Transmitter (km)
Gro
un
d C
on
du
cti
vit
y (
S/m
)
ILA-36 Orlando, FL October 2007Avionics
Engineering Center
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Terrain Smoothing over “Worst Case Path”
-1000
0
1000
2000
3000
4000
5000
6000
7000
0 100 200 300 400 500 600 700 800
Distance from Transmitter (km)
Terr
ain
Ele
va
tio
n (
m)
+3000
+2000
+1000
ILA-36 Orlando, FL October 2007Avionics
Engineering Center
21
Effect of Terrain Smoothing over WCP
-0.5
0
0.5
1
1.5
2
2.5
0 100 200 300 400 500 600 700 800
Distance from Transmitter (km)
AS
F (
mic
roc
sec
on
ds
)
ILA-36 Orlando, FL October 2007Avionics
Engineering Center
22
Effect of Receiver Altitude on ASFs over WCP
0
0.5
1
1.5
2
2.5
0 100 200 300 400 500 600 700 800
Distance from Transmitter (km)
AS
F (
mic
ros
eco
nd
s)
ILA-36 Orlando, FL October 2007Avionics
Engineering Center
23
Effect of Receiver Altitude on ASFs over WCP
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0 100 200 300 400 500 600 700 800
Distance from Transmitter (km)
AS
F R
ela
tiv
e t
o G
rou
nd
ed
Re
ce
ive
r (m
icro
sec
on
ds
)
ILA-36 Orlando, FL October 2007Avionics
Engineering Center
24
Terrain Contributions to ASFs over WCP
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
3
0 100 200 300 400 500 600 700 800
Distance from Transmitter (km)
AS
F (
mic
ros
ec
on
ds
)
ILA-36 Orlando, FL October 2007
Avionics Engineering
Center
Reality Checks
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Engineering Center
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Loran-C Correction Tables
Published by NOAA Show ASF corrections to TD values for
master-secondary pairs Cover US coastal confluence zones Data represents the results of a computer
program, adjusted to fit measured data
ILA-36 Orlando, FL October 2007Avionics
Engineering Center
27
Sample Loran-C correction table data
ILA-36 Orlando, FL October 2007Avionics
Engineering Center
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Terrain in the US West Coast region
Ground conductivity Terrain elevation
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Engineering Center
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Calculated ASFs for Fallon and Searchlight
Fallon Searchlight
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Engineering Center
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Correction table data vs. BALOR results
Loran-C correction table data Relative ASF data from BALOR
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Engineering Center
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Flight path from Ohio toward Carolina Beachtransmitter is Carolina Beach; aircraft is King Air; 8/29/07
The plot at left shows flight path; the color represents ASFs. Terrain elevation and conductivity are shown above.
0
200
400
600
800
1000
1200
1400
100200300400500600700800
Distance from Transmitter (km)
Ter
rain
Ele
vati
on
(m
)
0
1
2
3
4
5
6
7
8
9
Gro
un
d C
on
du
ctiv
ity
(mS
/m)
ILA-36 Orlando, FL October 2007Avionics
Engineering Center
32
Comparison of measured and calculated ASFs for flight from Ohio toward Carolina Beach
-1.0
0.0
1.0
2.0
3.0
4.0
100200300400500600700800
Distance From Transmitter (km)
AS
F (
mic
roseco
nd
s)
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Engineering Center
33
Approach to Allaire Airport, Belmar/Farmingdale, NJtransmitter is Carolina Beach, aircraft is King Air; 4/10/07
Flight Path Calculated Map of ASFs
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Engineering Center
34
Comparison of measured and calculated ASFs from Carolina Beach during approach to Allaire, NJ
1.5
2.0
2.5
3.0
3.5
4.0
0 20 40 60 80 100 120 140 160 180
Sample Number
AS
F (
mic
roseco
nd
s)
ILA-36 Orlando, FL October 2007
Avionics Engineering
Center
Closing
ILA-36 Orlando, FL October 2007Avionics
Engineering Center
36
Conclusions Further comparisons between BALOR and
actual measured data are required. It may not be possible to obtain extremely
accurate ASF predictions, due to lack of detail and possible bias in the conductivity database.
Nevertheless, we should be able to eliminate any bias or scale errors from the BALOR model itself.
Even in its current state, BALOR is a useful tool for large scale mapping of predicted ASFs.
More accurate results could be produced by adjusting the BALOR maps to fit measured data points.
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Engineering Center
37
Acknowledgements
Mitchell Narins, FAA, sponsor David Diggle, OU Avionics Engineering
Center, supervisor Wouter Pelgrum, Exian Navigation
Solutions, developer of the Loran TOA Measurement System (TMS)
Paul Williams and David Last, originators of the BALOR model
ILA-36 Orlando, FL October 2007
Avionics Engineering
Center
Questions?