How to calculate Area Under Curve?

Discuss roast levels and profiles for espresso, equipment for roasting coffee.
GDM528

#1: Post by GDM528 »

I briefly reviewed Artisan's documentation, and it appears the Area Under Curve (AUC) calculation is linear: units are Temperature-Time. There is an entry for base temperature, but again that appears to be a linear offset.

I keep using the word "linear", because chemical reactions generally have a non-linear relationship to temperature (e.g. Arrhenius equation) and a temperature threshold (technically, activation energy) before kicking in. So, roasting the beans at 100C for two minutes is not going to produce the same result as 200C for one minute.

Question: Did I misread the Artisan docs; does their AUC in fact actually incorporate something like the Arrhenius equation?

I get that an exact calculation would be impractical given all the different chemical reactions happening during a roast, but perhaps there's some way to approximate the exponential effect of temperature?

Marcelnl
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#2: Post by Marcelnl »

I interpreted the AUC as area under the curve representing power/energy going into the beans.

It computes as the area underneath the bean mass temperature (BT) curve and above a certain base temperature, starting from the begin of the roast or a certain well-defined point into the roast (like the yellow point marked DRY in Artisan) up to the end of the roast (marked as DROP in Artisan)
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CarefreeBuzzBuzz

#3: Post by CarefreeBuzzBuzz »

GDM528 wrote:
Question: Did I misread the Artisan docs; does their AUC in fact actually incorporate something like the Arrhenius equation?
The blog article may explain what you are looking for. Always check the blog for more technical material.
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GDM528 (original poster)

#4: Post by GDM528 (original poster) »

I saw the Artisan blog post on AUC - it's dated 2016. Per that post, the AUC result is simply Time x Temperature. I was hoping there was something more in the six years hence. As it is, is does provide a measure of cumulative applied heat energy, as long as things that affect heat transfer are held constant, like fan speed. Even then, if I match AUC I can still get significantly different roast results by changing the shape of the roasting temperature curve.

Windowing the AUC for each roasting phase helps a lot by partitioning the temperature ranges. I do the same on my spreadsheets but can still be fooled when trying to match roast profiles.

Marcelnl
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#5: Post by Marcelnl »

I'm more and more convinced that drop temp, time after FC and total roast time are more important parameters than AUC, you can roast to f.e 300 AUC by maintaining one low temp for incredibly long and end up with slightly heated greens.
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CarefreeBuzzBuzz

#6: Post by CarefreeBuzzBuzz »

GDM528 wrote:I saw the Artisan blog post on AUC - it's dated 2016. Per that post, the AUC result is simply Time x Temperature. I was hoping there was something more in the six years hence. As it is, is does provide a measure of cumulative applied heat energy, as long as things that affect heat transfer are held constant, like fan speed. Even then, if I match AUC I can still get significantly different roast results by changing the shape of the roasting temperature curve.

Windowing the AUC for each roasting phase helps a lot by partitioning the temperature ranges. I do the same on my spreadsheets but can still be fooled when trying to match roast profiles.
You answered your own question. People haven't found it that useful. You can always make a feature request if you think it can be improved.
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GDM528 (original poster)

#7: Post by GDM528 (original poster) »

I just reviewed the current Artisan code on github: AUC is still calculated as per their 2016 blog post, that is, linear temperature x time.

I don't use Artisan, so doesn't seem my place to be making requests to the devs. I was simply looking to the wisdom of Artisan for guidance on my own spreadsheet-based AUC calculations. I'll continue to experiment with AUC algorithms via spreadsheets before making any suggestions.

I hold out hope that AUC can be made more useful. Even now, a simple linear/windowed calculation has been instrumental in helping me understand roast differences and predict the outcomes of new roasting experiments.