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# Calculating formulation for new product with adjusted Bx Content

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### #1 rccz

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Posted 11 September 2019 - 11:10 AM

Good day,

I've been asked to assist a client with the following request and I've worked on a solution but I'm stumped as I'm getting confused with Bx and concentration.

Client currently has the following formulation for creating a Ready-To-Drink Lemon Drink of 12%.

They have a Lemon concentrate of Brix 30-32 and Acidity (%ACA) of 17-19%.

To create their RTD juice of 12% solution , the following ingredients were used:

Lemon Base (from above) 30.8g

Dry Sugar 70.4g

Water 898.8g

-Creating a 1000g solution with the final parameters of Brix 12 and Acidity (%ACA) 0.50%.

They have asked what are the adjusted amounts of the above ingredients needed to create a solution of of 10% and another of 15%.

(From my understanding, a solution of Bx 12 has 12g sugar in 100g solution but a concentration of 12% accounts for all solutes in the solution, both sugar and lemon base so I'm unsure how to proceed).

I want to work on the assumption that all solutes in solution are represented under the Bx of 12 and therefore, Bx 12= 12% concentration.

But then if I add the lemon base and dry sugar as my total solutes in solution, [(101.2g/1000g) x 100%] it gives a concentration of 10.12% and not 12%.

Alternatively, if i divide the 101.2 by 898.8 (total water) and not 1000 (total solution), I get a concentration of 11.25% which is closer.

I am stumped and unsure if I'm going about this the right way.

Lastly, will the acidity remain at 0.50% if I derive a solution of 10% and 15%?

Guidance is appreciated.

Guidance is appreciated.

### #2 pHruit

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Posted 11 September 2019 - 11:58 AM

"Brix" in the context of fruit juice has been somewhat misappropriated, so care is required when considering using it as a measure of sugars.

Consider, for example, the lemon juice from which your 30-32Bx conc was made - this will probably have had a Brix value of around 8, but the sugar content will potentially only be 1.6g (based on the latest McCance & Widdowson dataset). The relationship between Brix and actual sugar content varies quite significantly between different fruit (and between different batches of the same fruit), so there is no solid rule here.

It's sometimes considered more appropriate to view Refractometric Brix values of juices as a measure of total soluble solids, rather than of sugars, but again this is something of an approximation.

Consider Refractometric Brix, even if then subsequently corrected for acidity - you're really measuring the refractive index of your sample using a beam of light, and then you or the software in your refractometer are looking up what this refractive index corresponds to in a table that shows the relationship between the refractive index of a sucrose/water solution, and the %w/w concentration of sucrose in that solution.

In reality it's therefore an approximation even for a solution composed of differing sugars (as would be found in fruit), and that's before you start considering the effect of the many other soluble components of the juice.
Acid is a fairly significant component of many fruits and it has quite a significant impact on refractive index, so this relationship is reasonably well characterised and can therefore be taken into account by measuring the acidity separately and then looking up the appropriate correction in a suitable reference table (I've attached one from the US Customs Laboratory just in case you don't have one).

As a rough approximation, the midpoint of your specification is 31 Brix and 18%w/w ACA, corresponding to a correction of +3.35, giving you a corrected Brix value of 34.35, or 34.35g soluble solids per 100g (ish, keeping in mind the above discussion on approximations ).

I'm struggling to see how this product has a final Brix value of 12, though.

Your ingredients that contribute to this are sugar (sucrose?) at 7.04%w/w and lemon juice concentrate at 3.08%w/w, so even if the lemon was 100% sucrose then your total sugar content would still only be 7.04 + 3.08 = 10.12%w/w, i.e. 10.12 Brix.

Is it possible that the "12%" element is actually the final juice content, rather than the Brix value?

30-32 Brix lemon juice concentrate is often taken as being 4x concentrate, so the 30.8g in the recipe would equate to 123.2g of single strength juice, or 12.3%w/w in this recipe, which I'd guess is almost exactly 12% juice when considered in terms of volume/volume.

If the juice content is the actual target factor then you just need to back-calculate from this target, although I'd clarify first whether this is a w/w or a v/v target.

e.g. for 15%w/w juice, you will need 150g of lemon in your 1000g recipe. At a concentration factor of 4, this is 150/4=37.5g of the concentrate.

And for the 10%w/w juice, 100g lemon in 1000g at 4x concentration is 100/4 = 25g.

This will have a corresponding effect on Brix and on the acid content, so another question for your customer is what would they like you to do about this, i.e. should the sugar content be left as-is, or should it also be adjusted?
The perceived sweetness/sourness of juices is often approximated as the ratio between the corrected Brix value and the w/w ACA content (the so-called "Brix/Acid Ratio"), so you'd need to up the sugar content slightly to maintain the same apparent sweetness level in the 15% juice product as compared to the current 12% one. Similarly you'd potentially want to drop the sugar for the 10% version.

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### #3 rccz

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Posted 11 September 2019 - 01:21 PM

Thank you @pHruit.  Your info was very helpful.

I thought the same @ trying to determine how their final Brix was 12 as I got 10.12 taking into account the total solute content of the solution.

Questions:

1. I don't quite understand where the correction factor of +3.35 came from.

2. I don't understand the concentration factor bit, as to how 4 was derived.

I will look into detail at the second solution you derived which generates a value closer to 12%.

Many thanks.

### #4 pHruit

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Posted 11 September 2019 - 01:44 PM

For your questions:

1) I've made the (hopefully correct) assumption that your 30-32 Brix Lemon is specified using uncorrected Brix, as this is general practice in the juice industry. There are a few exceptions such as 66 Brix Orange Conc that is frequently specifified using corrected rather than uncorrected Brix, but it's not something I've ever seen used for 30-32 Brix lemon (and I look at quite a lot of juice ). So to get the corrected Brix value, which for most purposes is treated as the "real" Brix value, you also need to take the effect of the acid content into account - for something like an apple juice this is probably largely inconsequential, but it's quite significant for a highly acidic fruit like lemon.

With the tolerance you've given of 17-19%w/w ACA I've opted to take the midpoint, and then used the table in Annex I of the USCL methods file that I attached - simply look up the 18% value in the "Citric Acid Anhydrous, Percent by weight" column, and read across to the next column to find the Brix value to be added to correct the Refractometric value for the effect of the acidity - in this case 3.35.

These corrections are always added, as citric acid always bends the light in the opposite direction to the sucrose component of the solution - i.e. the effect of citric acid is to artificially reduce the Brix result compared to the "real" value.

2) The concentration factor is based on how much single-strength juice can be made from a given quantity of the concentrate. As you're in the UK, a reconstituted juice is obliged to meet the minimum Brix requirements defined in Schedule 13 of the Fruit Juices and Fruit Nectars (England) Regulations 2013 (and/or the appropriate equivalents for Scotland, Wales etc), which in a more general sense are the local implementation of Directive 2001/112/EC, as currently amended by Directive 2012/12/EU.

If you read these regulations/directives (and I'd highly recommend it as they are a gripping page-turner ) you'll find that the entry for Lemon Juice from Concentrate requires a minimum Brix of 8.0.
Thus for a 32 Brix concentrate, 32/8 = 4, in a rough nominal sense - i.e. 1kg concentrate is equivalent to 4kg of single strength juice.
It's not quite that clear-cut, as in reality even at the bottom of the spec at 30 Brix and 17% acid, the corrected Brix value is around 33.2, and 1kg of this is actually equivalent to about 4.15kg of juice at the minimum Brix.

It's worth noting that the regulations don't specify a maximum brix value though - the purpose is largely to ensure that consumers aren't being ripped off with over-diluted juice - so as long as you're above 8.0 then you're fine. It is thus somewhat conventional to aim to slightly underestimate the juice content as that way you're always erring on the compliant side of things with the regs.

This becomes more critical if you're working with massive volumes, so for example the sites that are packing hundreds of millions of litres of from-concentrate orange/apple/pineapple etc for the major retailers will take a bit more care in adjusting this and fitting into a very tight tolerance, but for more modest scales the approximation of this type of lemon being a 4-fold concentrate is very reasonable.

### #5 rccz

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Posted 12 September 2019 - 09:55 AM

Hello @pHruit.

I slept on this last night and did some research based on your recommendations. What you said about the 30-32Bx equating to 4x concentration makes sense to me.

My issue is, I don't know how to calculate the new acidity based on the change in ingredient weight or how much it changes by.

For example, if we're making the 10% juice, we adjust the lemon concentrate to 25g, while keeping the dry sugar content stable at 70.4g (disregarding desired taste for now) and adjusting the water so the solution volume is constant at 1000g, how do I calculate what the new acidity is?

In the client's information, the acidity of the concentrate was 17-19%ACA and the acidity of the 12% juice was 0.50%. How is this derived? Can I calculate it without doing lab tests?

It appears to me that the 12 degree Bx does not have a relationship to 12% Juice solution because when I used Bx to determine concentration, I got 10.12% which was incorrect. Therefore, is there a way to determine Bx from this formulation as well?

Thank you.

(Separately, is there an online course or any manual or anything I can read to get a better understanding of this stuff? Or are you happy to be bombarded by my many questions?  )

### #6 pHruit

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Posted 13 September 2019 - 09:02 AM

Apologies in advance for the exceptionally long post…

In the context that you’re considering, think of Brix and juice content as being completely independent.
It is possible to make a 12% lemon juice product at 12 Brix if you add the right amount of sugar, but it’s also possible to make a 12% lemon juice product at 2 Brix (it’s be a bit flavourless and slightly sour), or at 28 Brix (it’d be disgustingly sweet) by adjusting how much sugar you are / aren’t adding.

For the acid, it’s relatively simple – ignore anything that isn’t contributing acidity, which in this case is everything that isn’t lemon.

Your lemon juice concentrate has an acidity of 18%w/w ACA, taking the midpoint of the spec, so this means that there is 18g of ACA in 100g of concentrate. It’s actually a bit more subtle than this – the figure actually relates to the total titratable acid quoted as anhydrous citric, but you can safely ignore that distinction in this context.

In your recipe for the 10% variant you are adding 25g of concentrate, so this gives you 18*(25/100)=4.5g of citric acid in your blend of 1000g, so this is (4.5/1000)*100=0.45%w/w.

Similarly for the 12% variant you have 18*(30.8/100)=5.544g total in 1000g, so (5.544/1000)*100=0.55%w/w.

(The 0.50% figure that’s quoted for this may be a nominal rounding?)

You can also take a similar approach with the Brix calculations to get yourself an indicative value, although it’s always best to verify this by analysis too

For your 10% variant you’re adding 25g lemon per 1000g, so (25/1000)*100 = 2.5%, and 70.4g sugar i.e. (70.4/1000)*100=7.04%. We’ll take the former as 31 Brix (assuming we’re going to continue working with uncorrected values), and for the latter 100 Brix.

The Brix “contribution” from each is therefore.

31*(2.5/100) = 0.775

And 100*(7.04/100) = 7.04

Summing the contributions gives an expected nominal value of 7.04 + 0.775 = 7.8 Brix for the blend.

For comparison the calculation for the original 12% version (30.8g concentrate per 1000g, so 3.08% in the recipe), the equivalent figures would be:

31*(3.08/100) = 0.955

And 100*(7.4/100) = 7.04

Summing the contributions gives an expected nominal value of 7.04 + 0.955 =  7.995 Brix for the blend.

Considering  the latter in terms of soluble solids instead would give:

30.8*(31/100)= 9.54g soluble solids

70.4*(100/100) = 70.4g soluble solids

Total = 70.4 + 9.54 = 79.94g solids per 1000g recipe, so 79.9*(100/1000) = 7.994g soluble solids per 100g, i.e. 7.994 Brix

(Tiny difference between 7.994 and 7.995 inconsequential – no sane person would quote three decimal places for a Brix value for this sort of product!).

The value for the current recipe isn’t unexpected given that the single strength Brix value for from-concentrate lemon juice is 8.0; I’d guess this was originally formulated to behave roughly as a sweeter substitute for pure lemon juice?

You could preserve the perceived sweetness by increasing both the lemon juice content and the sugar content (as mentioned previously, the perceived sweetness is largely down to the ratio of sugars to acids, rather than the absolute values), but higher sugar content will also affect mouthfeel, and lemon is naturally quite a “thin” juice.

As for online courses, I’m afraid I have no idea!

I learned much of this from a mentor early in my career and by teaching myself, and for my staff and others in the business I deliver the training. For general juice familiarity I know that the BSDA does a course on juice processing that covers many relevant things, and it’s delivered by some truly excellent and fantastically knowledgeable tutors. Next one is in a few days: https://www.britishs...nufacture/44184

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### #7 rccz

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Posted 13 September 2019 - 02:19 PM

This has all been very helpful, thank you.

You mentioned you deliver training, is this only on-site or do you conduct webinars or online training sessions as well?

Thanks.

### #8 pHruit

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Posted 13 September 2019 - 03:11 PM

Unfortunately I'm only allowed to deliver training within my employer's businesses, or the occasional industry association (rude to say no if they've invited you...) - my current contract doesn't permit me to undertake any work for other food businesses without getting prior approval, and the chances of getting approval for work that is in a sector that is close enough to actually make use of my knowledge is alas extremely slim

### #9 rccz

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Posted 13 September 2019 - 03:24 PM

That's quite alright.

I'll attend the course on Juice manufacturing, it looks helpful.

Again, thank you for your help!

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