FDC
Runway Resolutions
on October 27, 2014

Many moons ago I wrote a Runway Resolutions blog about how to calculate the position of the aircraft on the runway during a landing. I said that we used the ILS localizer signal where it is available to give a better indication of the position of the aircraft when compared to the recorded position information.

Recently a customer showed me the trace of a near runway excursion where the aircraft had landed in a crosswind and put one wheel beyond the white runway edge marking. Fortunately there was a hard apron to the runway so the aircraft turned back towards the centre of the runway and what could have been a serious accident was simply another incident to remind us of the risks of runway excursions.

The incident led me to wonder how good the localizer signal is, and whether it is always better than the recorded position data.

Bear with me – here come some dull conversion formulae which will result in a sensible conclusion.

## Latitude and Longitude

Typically, recorded latitude and longitude information is stored in three 12-bit words, giving 18 bits for +/- 180 degrees. To convert from longitude to a distance on the ground, we’d have to worry about the latitude of the airfield (because the earth is round. Things would be so easy if only the flat earth society was right).

Let me keep this simple and we will imagine a runway running East-West, so to convert the recorded position resolution to a distance on the ground we only have to work with the latitude.

The latitude is normally stored in 17bits. One bit is the north/south sign bit, so 90 degrees is represented by an integer between 0 and 216, or 65536. That is, 0.001373 deg/bit.

A degree of latitude is 60 nautical miles, and a nautical mile is 1852 metres, so we have a resolution of 152 metres per bit.

## ILS Localizer

Unless you are an ILS antenna specialist, I can think of few things more dull than an antenna array, but here is a photo so you remember what we are talking about.

The signal received in the aircraft is two modulated signals and the deviation from the runway centreline is detected as a difference in the depth of modulation (ddm) between the two signals. This is then displayed to the pilots on a scale with two dots either side of the midpoint.

The scaling for ILS localizer signals varies with the geometry of the runway, so let me again simplify things by assuming our East-West runway is 50 metres wide and 2500 metres long. At this proportion, the localizer scaling is 1.252 degrees from the runway centreline per dot.

Typical the flight data recorder ILS scaling is 0.000781 loc-ddm per bit, corresponding to 0.0101 dots per bit. Using the scaling above, this is 0.0126 degrees per bit and, again using our 2,500 m runway, this corresponds to 0.54 m per bit at the threshold.

## Comparison

Using the recorded latitude and longitude of the aircraft, the resolution is 152 metres per bit. Ignoring errors in the navigation system, we only record in jumps of 152 metres.

By comparison, the ILS signal recording varies in jumps of 0.54m, or 1/300th of the size.

In a nutshell, using the ILS signal to compute the position on the runway is about 300 times more accurate than using the recorded latitude and longitude.

TTFN

Dave

## Epilogue

Some very new aircraft record position data with greater precision, using 24 bits rather than 18, but even so the ILS is still five times more accurate.