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Avionics Engineering

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Computer Modeling of Loran-C Additional Secondary Factors

Janet Blazyk, MSDavid Diggle, PhDAvionics Engineering CenterOhio University, Athens, OH

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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.

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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)

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US Ground Conductivity Map

“M3 map” from CFR Radio and Television Rules (47 CFR 73.170)

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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

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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)

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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.

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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.)

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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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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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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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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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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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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

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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

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Avionics Engineering

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“Worst Case Path” Examples

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“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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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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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

)

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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

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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

)

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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)

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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

)

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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

)

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Avionics Engineering

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Reality Checks

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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

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Sample Loran-C correction table data

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Terrain in the US West Coast region

Ground conductivity Terrain elevation

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Calculated ASFs for Fallon and Searchlight

Fallon Searchlight

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Correction table data vs. BALOR results

Loran-C correction table data Relative ASF data from BALOR

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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)

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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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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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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)

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Closing

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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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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

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Questions?