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The Instrument Landing System (ILS) gives output in terms of Difference in Depth of Modulation (DDM) to the avionics. But all display uses dots, also TAWS system definitions also uses dots as reference.

There is a generic convention that 0.175 DDM is 2 dots. This is why one dot is 0.0875 DDM and this value is the range for boundary used in ILS. Is there any formal reference for this conversion? I am looking at ICAO Annex 10, but could not find any relations yet.

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The problem you're having is that there is no standard definition of dots. There are various standards that come into play and I'll try to explain how they fit together.

As you noted +/- 0.175 DDM is specified as "full-scale deflection." This is in Annex 10 and, as mins noted, DO-192 for glideslope. It's also in DO-195 for localizer.

But what is 0.175 DDM and why is it referenced as "full-scale"? DDM is the Difference in Depth of Modulation of the 90 and 150 Hz audio tones that comprise the LOC and GS signals. The significance of 0.175 DDM is it defines the value at the limits of the course deviation display (full scale).

Annex 10 requires the installation of an ILS requires (for most runways) the radiation pattern of the localizer to place full scale at the threshold of the runway at +/- 350 feet. With the LOC antenna at the other end of the runway, this sets the angular deviation guidance for the approach.

This standard means that shorter runways will have a wider LOC beam than a longer runway. There are minimum and maximum angular widths, so very short runways (<~3000 ft) will all have the same maximum width and very long runways will have the minimum width.

Back to the ILS MOPS (DO-192 and DO-195). The MOPS has a standard for display of deviation in terms of centering accuracy (0.0 DDM) and linearity of the display out to "full-scale". Even if the display isn't part of the ILS receiver it's bound by the MOPS. In this case (which is common today), the radio is tested to comply at the "output to the display" and must have an interface spec to allow a display to be interfaced. The display - even if it's part of a glass PFD - has to meet the MOPS. And after installation they have to be tested to show they work together within the spec.

But what about the dots? The MOPS don't specify what the display looks like. The requirement is that the pilot can discern the center, the limits, and that the indication is linear within a few percent. Dots are not specified or required.

You identified a generic convention of 2 dots at full scale. I would agree this is common on air transport aircraft. But the GA aircraft I learned to fly in all had 4 dots on the CDI at full scale. And to be even more confusing, many of the new RNP deviation displays don't have any dots, just a bar with a center and end marks with the steering line on top.

In over 20 years of working in avionics, I've never found anyone who could say definitively why 2 dot displays became standard. My suspicion is that flight standards (and airline op specs) typically call for a missed approach if the deviation exceeds half scale. The 2 dot display puts a dot at that point and at full scale. It makes for good human factors. Getting the needle inside the outside dot means you've captured the signal. After getting on course, a deviation out to the first dot means it's time to go missed.

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