FDC
When is a Sample Rate not a Sample Rate?
on July 12, 2019

That is the question. Whether it is nobler… OK, let’s stop quoting Shakespeare and get down to engineering.
It is common for us to talk about sample rates as 1Hz, 2Hz etc. and in flight data recording we are usually talking about sample rates that are powers of two. If we have a parameter at 8Hz there will be eight samples in every second, and each sample will be 1/8th of a second after the preceding sample, and 1/8th of a second before the following sample. This principle of equal spacing is fundamental to the purpose of making multiple samples. If we plotted the sampling time in seconds from the start of a frame for eight samples, we would expect a plot like this:

## The Story Starts Here

In a recent example, our data specialist noticed an abnormal trace in the pitch signal. His original cause for concern was this plot:

This plot shows the pitch attitude at liftoff, where the signal should rise smoothly to about 20deg, but the ragged edge is abnormal. This aircraft has multiple different sources for pitch, which is why there are multiple lines drawn, but the blue signal is the one of interest here.

## Data Sources

For this aircraft, the documentation lists eight “Pitch Attitude” parameters from the DMC source, eight “Pitch Angle” parameters from the IRS source (with coarse and fine parts) and four “Pitch Angle” parameter from an ISISI source. As an aside, the Pitch Angle is a different signal from the other two, and I have not yet taken time to understand what it means. Still, I digress.

The word locations are irregularly spaced in the 1024-word frame, for example the IRS coarse data is found in words

Clearly these are not spaced evenly across the frame in the conventional manner, but the location of the word need not match the moment that the parameter is sampled, so these could still be equispaced samples, just stored in an unusual pattern. Unfortunately, the data frame documentation does not tell us anything about the timing of the samples, so we need to work this out for ourselves. A piece of reverse engineering gives the answer.

## Reverse Engineering

Knowing that the aircraft pitches progressively during the takeoff, we can compute an error function as the difference between the sample values and a best fit straight line to the data. We then allow each of the eight samples to have an offset in time and find the eight offsets which give the minimum error. Clearly the offsets (due to latency) have to be positive, as you can’t know the future.

For those who want to try this for yourselves, here is the data I used from one flight. It covers eight samples over eight seconds. Excel with the Analysis Toolpack option added and the “solver” function will do the job.

My calculation gave these latencies:

Note that IRS_1 is assumed to have no latency, and the other samples have huge delays in measurement. If we translate these into the time at which the sample was taken compared to the start of the frame, like the chart at the top of the blog, we have the astonishing:

That is, four of the samples have such latency the measurement was actually taken in the period of the preceding frame. What is not obvious at first glance is that the range of sample timings from -0.15 to+0.2 seconds only covers 0.35 seconds. That is, all eight samples have been measured within a 350mS period. The result is that our pitch trace, with sample timings corrected looks like this:

## The Story Ends Here

We did not spend the time necessary to find out if this pattern of latencies is repeated on other flights, or if it changes from flight to flight. We just decided that it’s an awful signal and we would just choose one sample and provide a pitch signal at 1Hz.

Fortunately, the data being used here is for engine performance monitoring, so the engine specialists only need to know if the aircraft is airborne or not, and so a low sample rate is good enough. Also, this data is from a DAR (non-mandatory) source so it does not matter from a certification or accident investigation point of view. The only “loser” here might be the airline who paid to have a signal recorded at 8Hz, not realising that eight samples need not be equispaced.