Theory and measurement don’t agree. Which is right?

The driver has to be of sufficient low Q to be able to get a Qtc that low. Sometimes drivers measure higher than spec. Sometimes more box damping is needed, or even an aperiodic vent. Sometimes the model was not done correctly by the user.

That website can be difficult to get everything entered "just so".

Inaccuracies input = inaccuracies output.
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If the driver TS parameters were properly measured out of box with DATS and the box volume is measured precisely, including subtracting the volume consumed by braces and the driver magnet and cone etc. I typically see good agreement. If you use the driver specs from the manufacturer or ignore the volume used by the driver etc. there will be differences. I typically use WinISD, and have not tried As I now use a Linkwitz transform on all my builds I can get the desired F3 and Q I want with active filtering.
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Yes, I often use the very practical online calculator, and usually when I check the FR of the realized enclosure, and compare to the simulation, they meet without significant difference due to unavoidable / unpredictable dispersions, that is to say a few Hz at worse.

But a gap in QTC from 0.5 to 0.71 makes a very significant volume difference of the enclosure !

None of the above, or all of the above.

To get all of these things lined up:

  • Measure T/S of the driver itself
  • Make sure you have the right volume, as well as all losses in volume + mechanical losses
  • Not clear from the context, but damping material has a big influence on this
  • Measure the total Q of the box with the same voltage/conditions you measured the T/S with

there are a few more steps/things, but those are already very significant.

- When a BR port is involved, get ready for a MASSIVE rabbit hole.

That is an entire new can of worms.
Thank you everyone for your input. I’m inclined to think that the measured Qtc is likely to be pretty accurate, since it’s a value derived from the peak value and -3dB bandwidth at resonance. I used the Scanspeak’s T&S values for the calculation, and although I don’t believe there’s a definitive way of deriving the values and I know that Scanspeak have changed the way they calculate them at least once, I’m surprised that the discrepancy is so great.
He's talking about how DATS is small signal and not enough power to register the larger signal parameters. DATS is USB driven at 5V, and current up to 1000ma. Larger signals drastically change how drivers such as these with large Mms, large Xmax, small Vas, and low Qts operate.
So how large a signal (voltage) and what amps (current) are we talking about?
Noob question : does one need to add mass or sealed volume to measure TS with DATS (or Arta box) ? Remember Earl G. iirc told about small voltage to be the best to measure TS. Do not remember what Dickason wrote about TS measurement. Half the mass of the cone added ?ambiant air (20 to 25°C), driver breaked in ?
Yes, added mass required to obtain all parameters. Add mass around same as Mms, or enough to lower Fs by 25%.

T/S is small signal parameters by definition, 100mV is enough really however many manufacturers test higher 1V+ because Fs will be lower.

All conditions, voltage level, ambient temperature, break in etc affect results, best to compare result of cabinet model rather than focus on any single parameter value, or the data sheet for that matter. If you can measure the parameters yourself with confidence, throw the data sheet away.

I’d recommend downloading VituixCAD for enclosure simulation, rather than simple website.
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2V is enough to exceed xmax on many drivers testing free air. Not only is it excessive, also makes it difficult to keep your added mass attached. There are plenty of good reasons to test a driver at higher voltage, gathering T/S parameters isn't one.

As much as I prefer a simple resistor jig over DATS, the DATS does at least enforce some consistency in measurements by removing user control over the signal level.