Back in 2018, Steve Smith wrote to me:

“Be careful of the time delay of exhaust gas pulsations arriving at the tailpipe in comparison to the exhaust valve open event.”

A fag-packet calculation showed Steve was dead right: taking the speed of sound in dry air at 150C as 400m/s and having measured the twists and turns in the (hatchback) exhaust system as 4.5m, we get 11ms, as a rough number for the time it takes for a pressure pulse to travel from the exhaust ports to the tailpipe on my vehicle. And, whilst, on my car this time lag equates to around 80 degrees of rotation at idle (see below), this lag becomes as much as around 270 degrees at 4000 rpm (see below). (The speed of sound isn’t too sensitive to temperature, so we’re not going to be far out, and certainly not by an order of magnitude.)

I’ve always kept Steve’s warning in mind, and now, whilst investigating an intermittent valve-sticking fault, I had the opportunity to look deeper into this.

The downpipe has a blanking plug opposite the oxygen sensor, just below the connection of the manifold to the downpipe. Using a Fluke pressure transducer inserted into the plug boss, and a pressure sensor (GM fuel-tank pressure sensor) in the tailpipe, the time lag through the exhaust system could be measured. (The traces themselves, and how they relate to the sticking valve, will be dealt with elsewhere.)

The traces from the Fluke transducer in the downpipe and the sensor in the tailpipe were searched for valve-sticking events that could act as markers.

The left-hand vertical ruler (below) marks a missing exhaust pulse in the blue trace, as detected at the start of the downpipe; the right-hand vertical ruler marks the corresponding point in the trace (red) at the tailpipe. The time lag is 12ms, which corresponds to 82 degrees of rotation at 1150RPM on a warm (57C) engine



The time lag only depends on the speed of sound in the exhaust gas and not directly on the engine speed, although a higher engine speed will produce a hotter exhaust so we could expect possibly a slightly smaller time lag.

At 4000RPM, with an engine temperature of 60C, we see a time lag of 11ms, but this now corresponds to a much higher 274 degrees of engine rotation. At higher engines speeds, the exhaust system has a large smoothing or damping effect on the pressure pulses, as if a very low-pass filter has been applied. Nevertheless, looking through the traces, I believe it was possible, with a high degree of confidence, to find an event (a noticeably high pressure pulse into the downpipe (left-hand vertical ruler) and match it to the corresponding pulse (red trace) at the tailpipe (right-hand vertical ruler).

Or again here, at 3850RPM, where a high peak in the blue trace (left ruler) corresponds to a clipped peak in the red trace some 10.8ms (268 degrees of rotation) later.
Therefore, it appears that 400m/s is a good estimate for the speed of sound in exhaust gas under normal conditions.

One other point concerns the coupling of pressure sensors and transducers; these must be DC coupled. If AC coupled, they appear to display rate of change rather than the change itself, so, for example, if a vacuum is applied and maintained and the device is AC coupled, the vacuum appears to rapidly fall to zero, whereas when DC coupled, the maintained vacuum continues to be recorded.

It’s pretty clear that a lot gets lost in translation by the time it reaches the tailpipe, so, where possible the downpipe is the place to tap into, but then again, not everyone has the resources to test there. But that’s for another day.

Hi Roman

Thanks for your kind words; I also learned a lot from it.

We all make assumptions all the time, and, most of the time, we’re not even aware we’re doing it until either something goes wrong, or, like Steve Smith did with me, someone challenges something you’ve said, and then you realise you’ve been making an assumption that was wrong. It’s a basic human failing. When I do it, generally the worst that happens is that I feel stupid, but when a pilot does it, they can fly the aircraft into the ground.

Pico call one of their exhaust-pipe pressure sensors a “first look” sensor, and that’s quite a clever name, because I still think - just like with the relative compression test - tail-pipe pressure pulses can be a very useful quick test to get a first impression, especially if you already have a known good to compare to. Even when I had AC coupling set, when I should have set DC coupling, and even without a good waveform for comparison, the exhaust tail-pipe pulses, using my home-made pressure sensor from a fuel tank (red trace below), showed there are serious problems on the exhaust side (valves not sealing properly - there should be 4 pulses per cycle, not 8 - and occasional valve sticking).
It may be that the exhaust tail-pipe pressure pulses don’t show exactly where the problem is, but they can give a rapid first look, to point you in the right direction for deeper diagnostic troubleshooting if necessary; in my case, however, it clearly told me that the cylinder head needs to be replaced/refurbished.

But your assumption about the silencer having a filtering effect is still correct.

If you also look into this and get some interesting results, especially with those big engines, perhaps you could share them?

Thanks again, Roman, for taking the time to add your comments.

Martin

. I’m now learning from you: I’m working my way through the Waveform Overlay topic, and then I’m going to track down your other posts. So, a big “thank you” in advance.

Martin