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Question on my sourdough hydration and build calculations, double checking

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CoveredInFlour's picture
CoveredInFlour

Question on my sourdough hydration and build calculations, double checking

Hi! I found in Jeffery Hamelman's Bread the section on "Building the Culture (also known as "Elaborating")", page 146, and while I'm pretty sure I understand it, I need some verification.

I started my rye culture, and have fed him, 1 measured cup rye flour with 1 measured cup bottled water according to the instructions given in The River Cottage Bread Handbook. What would have been, if I weighed it, 227gr water and 120gr dark rye flour.

I was happy not knowing the hydration % until I came up against it on JMonkey's post, "Lesson: Squeeze more sour from your sourdough".

He states, "The most common consistency is to have equal weights of water and flour, also known as 100% hydration because the water weight is equal to 100% of the flour weight. That’s roughly 1 scant cup of flour to about ½ cup of water. Jeffrey Hamelman keeps his at 125%, and quite a few folks keep theirs at 200% (1 cup water to 1 cup flour)."

However, when I do the math, I come up with a hydration ratio of 189:
(227g water/120g flour)x100)
(227/120=1.891) x100=189%

Now I'm assuming that in every hydration flour is always 100 units, so therefore water would be 189 units. Isn't that a 189% hydration?

Using that number, if I do the math for creating 400g of mature stater from 30 grams of seed at the same 189% hydration, for example, according to the method described in Hamelman's Bread the calculations to figure out how much water/flour I would need to add would go like this:

  1. The total number of units in the 189% hydration would be 289: 100 units flour + 189 units water= 289 total units.
  2. I would use the formula 370/289=1.28 . That is, the 370 grams more starter needed divided by the total amount of units in the hydration.
  3. Then I would multiply that by the 100 units of flour, so 1.28x100=128.03 grams of flour.
  4. Doing the same for the water, 1.28x189= 242 grams of water (really 241.92).

So, to wrap it up, is my seed culture of 1 measured cup flour to 1 measured cup water really 189% hydration and not 200%?

And to "grow" 400 grams of mature starter from 30 grams of seed culture at my 189% hydration I would feed it 128.03 grams of flour and 242 grams of water?

My sincere apologies if this topic has been beaten to death, I really do think I understand the calculations, I just wan tto double check that how I'm interpreting the information is correct. :)

Update:

I just checked Rose Levy Berenbaum's The Bread Bible, she gives the weight of 1 cup of water as about 237 grams. The hydration formula would then be (if we use that number) 237/120=1.975, rounding up to 200. So the total units would then be 100 flour + 200 water for a total of 300 units?

PastryPaul's picture
PastryPaul

First of all a cup of water is 240ml, therefore 240 grams.... although I won't quibble with 237.

Flour is always 100% and hydration is measured in relation to it by weight not volume. You are quite correct in saying a cup of water to a cup of flour is about 200%. If we replace your 227g of water with 240, your hydration becomes 200% as well. Also flour is not just flour when it comes to weight / cup. Different types and different brands weigh different amounts. My AP flour is 128 grams to the cup, so it would be 187.5%

Simplify your math. If you need to determine ingredient weights from a set formula, you can switch over to yield percentages if you like.

Therefore, flour would now be expressed as 34.6% of yield (100 / 289 total BP), while water is 65.4% of yield (these are based on total yield not Bakers' Percentages). It is now a simple matter to decide on the yield you want and apply those percentages.

You want a kilo? Use 346g flour and 654g water. You want 370g? 370 X 34.6% = 128g flour, 370 X 65.4% = 242g

If you prefer to remain in BP use this formula....

(Desired Yield / Total BP) * Ingredient BP = Ingredient weight

So... with a desired yield of 370g, total BP of 289% and 189% hydration

(370/289) * 100 = 128g flour (always 100%, if several different flours they will add up to 100% so use each flour's BP)

(370/289)*189 = 242g water

Hope this helps

CoveredInFlour's picture
CoveredInFlour

WOW! Thank you!!

I have read about 4 different weights for 1 cup of water;  227 grams, 237 grams, 240 grams and 255 grams (that last one seemed a bit high); I wasn't sure which one was accurate.

I've never really had luck with baker's percentages, even my husband who minored in Math in University doesn't understand the formulas. But I really appreciate it you adding it, I'm printing it out and will work through it step by step.

I'm not a stupid person, but I find a lot of the formulaic math work in baking bread difficult to understand. Well, maybe I am stupid. :)

Thank you again, this helps very much!

PastryPaul's picture
PastryPaul

The first time I saw BP I was royally confused! How could anything be greater than 100% of itself???

Once you get the hang of basing everything on flour weight, it quickly falls into place.

Re Water weight... it's fairly simple. A mililiter is defined as a cubic centimeter. A gram is defined as the weight of a cubic centimeter of water. Therefore a milliter of water weighs 1 gram.

That becomes the basis for all volume to weight conversions. If you can get your hands on the specific gravity of anything, you can work out what a cup of it would weigh. Specific gravity is what something would weigh for the same volume of water. Since my AP flour's specific gravity is 53.33, a cup of it would weigh 53.33% of 240g, 128g

Cheers

CoveredInFlour's picture
CoveredInFlour

"How could anything be greater than 100% of itself???" That EXACTLY what he said!!

I've generally never been good at anything more than basic math, probably because I never had it taught to me in a way I can understand it, i.e. NOT the public school method. I had a tutor for algebra in high school, that was the only time I ever understood it. Luckily my daughters are MUCH MUCH better at advanced math!

Now I'll have to look up the specific gravity of ALL my flours! :D

 

placebo's picture
placebo

A cup is a measure of volume, equal to about 237 ml. The weight* of 1 ml of water is 1 gram, so a cup of water weighs 237 grams. The 240-gram figure is just 237 grams rounded up.

The 227-gram figure results from confusing an ounce, which is a unit of weight*, and a fluid ounce, which is a unit of volume. A fluid ounce of water weighs 1.043 ounces, so a cup of water weighs 8.34 ounces. If you mistakenly assume a cup of water weighs only 8 ounces, you're underestimating its weight by about 4.3%. Reduce 237 grams by 4.3% and you get 227 grams.

I'm not sure how someone would come up with 255 grams for the weight of a cup of water. I found it is approximately the weight of a cup of 100%-hydration sourdough starter. Perhaps that's where that number came from.

 

[*] Most people incorrectly use grams and ounces as a measure of weight, but they are really units of mass. 

MangoChutney's picture
MangoChutney

It depends on how many fluid ounces are in the cup in question.  One fluid ounce of water weighs one ounce within the precision of a measuring cup.  One ounce equals 28.35 grams.  But cups range from 8 fluid ounces (226.8 grams of water) to 10 fluid ounces (283.5 grams of water), because the definition of a gallon has changed according to the politics of British royalty.  The cup which is 8 fluid ounces was based on gallons which fit evenly in a cask of wine, while the cup which is 10 fluid ounces is based on gallons that fit evenly in a barrel of ale.  At the time of the change, wine was a beverage imported from France, while ale was domestic.  The change reflected a transfer of royal favor to local economics.

Chuck's picture
Chuck

I think all your math is correct  ...once the correct weight of a cup of water is used and a bit of rounding is allowed, as noted by previous posts. But it should be much easier than you make it seem (bakers percentages are supposed to be easier, not harder). You're dealing with the very hardest case for bakers percentages: a starter, as well as the final dough, and shooting for a total yield rather than a total flour weight. (If someone wanted to cast bakers percentages in a bad light, this is the case they'd use. Nothing else will ever be harder.)

Anyway, my suggestion is to get a spreadsheet that allows you to input the numbers that make sense to you (maybe starter hydration, amount of starter, desired overall hydration, and desired total yield). Then let a computer do the funky calculations.

Yes the idea of bakers percentages basing their 100% on the weight of flour rather than the total weight is contrary to the usual definition of percentages and to many expectations. But there are good reasons for bakers percentages being that way, and they really are very convenient in many cases. In my experience, the trick is to take what you "already know" about percentages, and throw it all out as not helpful in this particular case. Once you do that, they're not too hard to grasp. You'll never manage to "mesh" bakers percentages with school math about percentages; it works far better to not even try - it's not a matter of being "bad at math"; they really don't line up.

PastryPaul's picture
PastryPaul

I have a spreadsheet that calulates on BP as well as calculating DDT

Any idea how to post it?

Cheers

CoveredInFlour's picture
CoveredInFlour

I created a spreadsheet last night for sourdough hydration %, it calculates how much water and flour you need for a given amount of final starter at any hydration percentage given:

I only need enter the amount of starter I want to end up with and the hydration % I want and it does the rest. If I have some culture I'm using to seed it (or if I'm in need of feed amounts), I add the amount of starter I'm using.

I'm going to try and create one for Baker's Percentages based on the information in Meggie Glezer's Artisan Breads.

BTW, Peter Reinhart gives 227 grams for the weight of 1 cup of water. Is it any wonder there is confusion?? *sigh*