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What is the outer marker "distance" along the flight path of a 3 degree ILS?

I provide my two approaches below, but as they contradict each other, I am asking this question to learn the proper answer.

Approach #1: Wikipedia says OM horizontal dimensions is an ellpsoid of 2400 x 4200 ft (I assume the former is the dimension parallel to aircraft's path ) at 1000 ft. I assume vertically OM signal is of conical shape, therefore its horizontal size expands and should be (proportionally) larger at higher altitudes. At 3 degree glideslope, altitude range for OM crossing is between 1200 and 2100 ft (4 NM and 7 NM respectively). This gives an answer to my question equal to a range between 2400 * 1.2 = 2880 and 2400 * 2.1 = 5040 ft.

Approach #2: Flying at 100 kts, I can hear OM for ca. 12 seconds at 4.4 DME. This translates to 2000 ft of OM length at height of 1500 ft. Empiria does not give a range, but still contradicts wikipedia and is much more reasonable number, as I cannot remember hearing OM for almost half a minute while flying over...

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    $\begingroup$ While the ideal model of the radio signal is concical, I believe the actual radio signal shape is closer to a paraboloid (egg shape). $\endgroup$ – Ron Beyer Oct 11 '16 at 14:40
  • $\begingroup$ That would be a good explanation, I like it. However, it would only fit the Wikipedia and empiric data if it the egg were less than 2000 ft high - decreasing size above 1000 ft :). So I still wonder if anybody knows the exact numerical solution to this question. $\endgroup$ – user2530062 Oct 11 '16 at 14:45
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As Ron Beyer commented, it's more of a flat ellipsoid (egg), not a cone.

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Full Image

Another site shows that image:

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From the United States Standard Flight Inspection Manual, the tolerances are:

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Minor axis being parallel to approach:

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    $\begingroup$ Thank you. I suppose it does not differ much for Europe and it allows for difference in width that - despite egg shape - may still come with different distances to threshold. With a keyword search for the minor axis of outer market I have also found information that the "optimal" value is 2000 ft. $\endgroup$ – user2530062 Oct 11 '16 at 19:09
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    $\begingroup$ The sensitivity of your marker beacon receiver will also affect things a bit. It's easier to draw the "shape" of the beacon as having a defined edge, but in reality it isn't a binary transition from "outside" to "inside" -- there will be an area where the signal strength increases as you enter "the cone" and another were the signal strength drops off as you leave it. While this ramping up & down will be fairly steep, it is there, and the number of seconds that one aircraft at 100 knots groundspeed is receiving it may vary slightly from what another aircraft gets. $\endgroup$ – Ralph J Oct 11 '16 at 20:38

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