Beersmith 3 ph tool

[Big Monk]

AJ's data? No I do not have it; I simply reconstructed an approximation to his data using the cubic fits (pH_i, a_0, a_1, a_2) that AJ has posted on this forum.

Do you have his data? Is it available somewhere?

I guess I’m confused now. Aren’t the cubic fits what matters? Don’t the cubic fits give the titration coefficients we need to calculate QMalt?

EDIT: I understand what you are driving at now about the initial data versus the fits.

Also, after rereading your Part III, it seems that you’ve made the assumption that, all things equal experimentally, the malts measured by each researcher would have identical values for titration co-efficiencts. While I’m inclined to agree up to a certain point, we shouldn’t really expect parity across all researchers data, should we? Malt is a product that varies from lot to lot. So then doesn’t normalizing data across all the researchers induce additional errors on top of not knowing why there were differences in the first place?

Malt is really the crux of the whole discussion and in some ways I agree with your argument that we may never have widespread data about the full buffering capabilities of malt. I’d love to get a campaign going addressed the maltster s to give this data. I know A.J. beat that drum some years ago to no avail but a coordinated effort from pro and Homebrewer’s alike could turn the tide.

 

[dmr]

I guess I’m confused now. Aren’t the cubic fits what matters? Don’t the cubic fits give the titration coefficients we need to calculate QMalt?

Yes, the cubic fits will clearly give you Q_Malt values. But I feel that most data is not of sufficient quality to reliably fit it to a cubic equation. AFAIK, only AJ's data is that good. Furthermore, if one uses a linear approximation to describe all titration data, then one has two parameters -- pH_i and B_i -- that can be compared (and averaged) among different researchers' measurements.

Also, after rereading your Part III, it seems that you’ve made the assumption that, all things equal experimentally, the malts measured by each researcher would have identical values for titration co-efficiencts. While I’m inclined to agree up to a certain point, we shouldn’t really expect parity across all researchers data, should we? Malt is a product that varies from lot to lot. So then doesn’t normalizing data across all the researchers induce additional errors on top of not knowing why there were differences in the first place?

If you look at part (b) of Fig. 7 in Part III, you will see that there is a clear systematic difference between each researcher's set of B_i's across all Briess Caramel malts. The main difference between any two researchers is clearly systematic, although there are also variations that can be attributed to differences in batches of malt.

That this systematic variation exists -- and can be corrected for -- is confirmed when the Briess-Caramel-malt derived correction factors are applied to all Caramel/Crystal/Dextrine, Base/Specialty, and Dark Roasted malts. As is shown in Fig. 8, when the correction factors are applied to all of the data from each researcher, there is a much better agreement in B_i values. To see this simply compare the spread in unadjusted B_i values (middle three panes of Fig. 8) with the spread in adjusted values (bottom three panes of Fig. 8).

So I believe I have produced a reasonable set of relative B_i values for the set of malts in Fig. 8. But what is the overall correction factor applicable to the typical homebrewer setting? I don't know. This is precisely why I have asked for brewers to post their mash pH measurements.

 

[Big Monk]

Yes, the cubic fits will clearly give you Q_Malt values. But I feel that most data is not of sufficient quality to reliably fit it to a cubic equation. AFAIK, only AJ's data is that good. Furthermore, if one uses a linear approximation to describe all titration data, then one has two parameters -- pH_i and B_i -- that can be compared (and averaged) among different researchers' measurements.

In a perfect world, we’d use:

dQMalt = a1 * ( pHz - pH DI ) + a2 * ( pHz - pH DI ) ^ 2 + a3 * ( pHz - pH DI ) ^ 3

to express each individual malts Q value.

In the case of the malts measured by some researchers, who willingly chose to forgo measuring a2 and a3 (this isn’t meant as an insult), the way to know whether neglecting to measure a2 and a3, and using only pH DI and a1, is effective is to mash them and compare estimated to actual.

Crystal/Cara malts, Roasted Malts, and Sauermalz will express the largest variation in QMalt between linear and polynomial calculations. I tried to show this above with my examples of A.J.’s Crisp 600L and Sauermalz values. In those cases, expressing them linearly will cause enormous swings in QMalt. To your point though, there are some malts that, even with the full range of co-efficients, will have a Q value very close to the linear approximation.

In my mind, and I may be stubborn here, you run this same risk with a malt where only pH DI and a1 are measured and used in a linear approximation of malt acidity, i.e. the a2 and a3 values are there whether you measure them or not and by using only pH DI and a1 to represent Q for that malt, you introduce the risk of overestimating it’s acidity.

I find this all so very interesting.

 

[dmr]

Crystal/Cara malts, Roasted Malts, and Sauermalz will express the largest variation in QMalt between linear and polynomial calculations. I tried to show this above with my examples of A.J.’s Crisp 600L and Sauermalz values. In those cases, expressing them linearly will cause enormous swings in QMalt. To your point though, there are some malts that, even with the full range of co-efficients, will have a Q value very close to the linear approximation.

Attached are some of my linear fits to AJ's data, including the 600 L Crisp Chocolate. After looking at the graph, you may feel that the linear approximations are inadequate. However, I feel like they are a pretty good description of the data in the range between pH_i and 5.3 to 5.5. Cheers!

P.S. I cannot remark on Sauermalz, as I have not looked at that malt.

 

[Big Monk]

Attached are some of my linear fits to AJ's data, including the 600 L Crisp Chocolate. After looking at the graph, you may feel that the linear approximations are inadequate. However, I feel like they are a pretty good description of the data in the range between pH_i and 5.3 to 5.5. Cheers!

P.S. I cannot remark on Sauermalz, as I have not looked at that malt.

If you mash with a large proportion of a roasted malt you feel has a decent linear fit, using a linear equation, and your estimated pH is much lower than your actual, you will have assessed how good the fit really is!

Also, am I understanding correctly when I say that for your fit of A.J.’s data, that a good fit means that the fitted slope and fitted pH are close to measured pH DI and a1?

For that malt, how would you then rectify:

Linear dQMalt = ~-155 mEq/kg

as opposed to

Polynomial dQMalt = ~-27 mEq/kg

 

[dmr]

Also, am I understanding correctly when I say that for your fit of A.J.’s data, that a good fit means that the fitted slope and fitted pH are close to measured pH DI and a1?

No, a good linear fit is one that reasonably matches AJ's polynomial fit, as it is AJ's polynomial fit that is being fit by the linear fit.

For that malt, how would you then rectify:

Linear dQMalt = ~-155 mEq/kg

as opposed to

Polynomial dQMalt = ~-27 mEq/kg

I don't know what math you are doing. For a pH of 5.4 I get -55.11 mEq/kg from AJ's numbers and -54.97 mEq/kg from my linear fit, consistent with the graph attached to my last post. As the difference is 0.14 mEq/kg, I'd say the linear approximation does a rather nice job.

 

[Big Monk]

No, a good linear fit is one that reasonably matches AJ's polynomial fit, as it is AJ's polynomial fit that is being fit by the linear fit.



I don't know what math you are doing. For a pH of 5.4 I get -55.11 mEq/kg from AJ's numbers and -54.97 mEq/kg from my linear fit, consistent with the graph attached to my last post. As the difference is 0.14 mEq/kg, I'd say the linear approximation does a rather nice job.

dQMalt = a1 * ( pHz - pH DI )

dQMalt = a1 * ( pHz - pH DI ) + a2 * ( pHz - pH DI ) ^ 2 + a3 * ( pHz - pH DI ) ^ 3

Straight from the man himself.

Maybe I’m misunderstanding what you are doing. How are you linearizing data that isn’t linear? Maybe it’s a semantic blockage on my part. When I say linear I mean what I show above. When I say polynomial I mean what I show above.

A.J. made measurements of those malts and the outcome was 3 titration co-efficients to be used in the polynomial equation above. Maybe I’m just missing something.

What formulas are you using to describe dQMalt (mEq/kg)?

 

[Silver_Is_Money]

The linear R^2 correlations are all indicating extremely good fits within the AJ Malts.PDF attachment as seen in @dmr's post above.

The formula derived for each "fit" is simply a standard linear slope and intercept equation in the form of Y= A +BX. Each lines equation is given in the PDF, along with its R^2 fit to the data.

 

[Big Monk]

The linear R^2 correlations are all indicating extremely good fits within the AJ Malts.PDF attachment as seen in @dmr's post above.

The formula derived for each "fit" is simply a standard linear slope and intercept equation in the form of Y= A +BX. Each lines equation is given in the PDF, along with its R^2 fit to the data.

So now the question is why do we think:

dQ = ( a1 * pHz ) + Fitted Constant

is a good representation of dQ?

 

[Silver_Is_Money]

I presume that the 'Y' Axis is mEq/Kg-pH, and that therefore (for any given malt which is represented on the chart) Y = mEq/Kg for any given pHz target.

So to put it all together:

Y = A +BX = mEq/Kg-pHz

Lets look at the base malt with a DI_PH of 5.6227 and for the target case of mash pHz = 5.4:

Y = 265.4 + -47.21*5.4 = mEq/Kg

Y = 10.466 mEq/Kg
(for the specific target mash pH of 5.4)

 

[dmr]

dQMalt = a1 * ( pHz - pH DI )

dQMalt = a1 * ( pHz - pH DI ) + a2 * ( pHz - pH DI ) ^ 2 + a3 * ( pHz - pH DI ) ^ 3

What formulas are you using to describe dQMalt (mEq/kg)?

Those that you have posted above, with the caveat that a1 in the linear equation is not the same as a1 in the cubic equation [as I've described in some earlier post (and can be seen in the pdf I posted)].

 

[dmr]

The linear R^2 correlations are all indicating extremely good fits within the AJ Malts.PDF attachment as seen in @dmr's post above.

So now the question is why do we think:

dQ = ( a1 * pHz ) + Fitted Constant

is a good representation of dQ?

The answer is summarized in Silver_Is_Money's statement.

 

[Big Monk]

Those that you have posted above, with the caveat that a1 in the linear equation is not the same as a1 in the cubic equation [as I've described in some earlier post (and can be seen in the pdf I posted)].

I re-did some calculations this morning and stand corrected (big time). I'm not sure what how i made that math error initially. I did it by hand and all my Excel coded dQMalt(a1,pHz,pH DI,a2,a3) functions show agreement with your numbers.

I have a feeling I may have swapped pHz and pH DI in the initial calculations.

Thanks for bearing with me on that one.

 

[Big Monk]

I’m potentially convinced that one cannot treat Sauermalz as a source of lactic acid.

Have you tried linearizing the Sauermalz titration info at all?

 

[dmr]

Have you tried linearizing the Sauermalz titration info at all?

Nope, I've not got around to thinking about Sauermalz. I'll need to do it at some point, though.

 

[Big Monk]

Nope, I've not got around to thinking about Sauermalz. I'll need to do it at some point, though.

As that’s my main acid source, I’d be interested in what you find.

 

[dmr]

As that’s my main acid source, I’d be interested in what you find.

Yeah, it is mine also, so I definitely plan to look into it.