## Calculating DDT considering mass.

Hi all.

Most recipes including in bakeries use a standart DDT calculation but I have never seen people considering the mass of each item.

So let's talk 60% dough (no salt, no yeast) Just water and flour.

Our DDT is 80

Formula would be

Flour 100 % 74F

Water 60% ?F (we are trying to find to get to DDT 80)

Total 160%

Standart way to calculate is 80 *2 = 74 + ?

Water comes out 86 .

But this is not realistic since mass of each item is different. This would work only for 100% hydration dough

We should first convert from bakers % to regular %

Flour 100/160 => Flour is 0.625% of the whole recipe.

Water 60/160 => Water 0.375 % of the whole recipe.

These should be used as coefficients to calculate the temperature.

80 = 0.625 * 74 + 0.375 * ? And the answer comes up to 90F

If this was 100% hydration dough

it would have been

80 = 0.5 * 74 + 0.5 * ? and the answer would be 86

So mass actually matters ? Is this an over kill.

I am thinking for places where they produce a lot of bread they must do the calculation like so.

But again huge productions lines are fully automated and computers are doing everything anyway.

But again how would ambient temp and friction factor would play into this ?

## 20200208_094653.jpg

That is modernist bread right. I have the book. I am gonna revisit.

Yes modernist bread. They don't specifically mention mass.

Hello everyone,

I think there is an error in the book, the fórmula only correct for degree Fahrenheit (°F). te number 38 in the formula refers to the specif heat capacity of flour, that is 0.38 BTU/(lb-°F).

For using the formula with temperatures in degree Celcius (°C), subtitute the number 38 for 64.5 (0.645 Kcal/(kg-°C).

So, for Celcius (°C):

Twater = DDT - DTfriction + 64.5 * (DDT - DTfriction - Tflour) / H

for Fahrenheit (°F):

Twater = DDT - DTfriction + 38 * (DDT - DTfriction - Tflour) / H

Regards

More on water temperature calculation.

Let say Cf and Cw are the specific heat capacity of flour an water respectively.

Then, the correct formula is:

Twater = DDT - DTfriction + Cf/Cw * (DDT - DTfriction - Tflour) / H

If we are using BTU/(lb °F), Cf/Cw = 0,380 and for Kcal/(kg °C), Cf/Cw = 0,645

Regards

I don't think the mass should matter in calculating the DDT. Since the mixed dough will come out at the DDT wether it's 500g or 5kg. Although a smaller mass would cool off faster than a larger mass.

But I didn't see you mention Friction Factor (FF), which is how much heat the mixers dough hook generates when mixing the dough.

I remember DDT as follows (example):

X3 = 234(then subtract the following)Room Temp = 73FFriction factor = 20FOr (RT+FL+FF)-234=69F water temp

Even if you are mixing by hand you would be adding a small bit of friction. I've used the above formula on different sized doughs and it was usually spot on when I was done. Keeping the dough at the DDT would require a proofing box.

I know the formula, I use it daily at the bakery.

We calculate the ambient and the FF for each dough on a white board.

We also have 5-6 years of data where we can compare against and data mind.

We are always a few degrees off(ddt math includes FF and all the other things you mentioned) And since water is always 80% hydration or more, it is weight(mass) is close the flour so the error rate is super low.

We always adjust by heart after years of working with the same recipes. Stuff goes into the proofer or moved by the oven to compensate for the fermentation speed based on the error in DDT.

But not once we thought about the mass of each ingredient (each ingredients' impact on the final dough based on their weights)

Think about a hypothetical situation where we are making a 500% hydration dough.

100g flour + 500g water.

If we use standard DDT formula, the numbers do not add up. As the heat impact of water is a lot more than the heat impact of the flour.

To even make a point let's think about 5000% hydration dough.

I know it does not make sense to make stuff up as it ll never happen but you ll see what I mean, with such little amount of flour vs so much water. Water would impact the DDT a lot more.

Mass of dough doesn’t directly affect DDT calculations. Indirect effect is that doughs with less weight reach DDT quicker in mixer than doughs with greater mass. So what bakeries do is adjust mixing times, not DDT.

The Modernist formula takes the hydration ratio into account. Seems logical to me, because if you have a higher ratio of water to flour, you don't have to get the water as hot to warm up the flour.

The formula includes the Cp values for both water and flour and thus compensates for the ratio of water:flour, but it does not compensate for different mixing conditions so you do have to keep book on each formula and each mixer (if want really good accuracy). The amount of energy that is deposited into the dough is a function of the dough temperature and the hydration and how long you mix. Cp is the conversion factor from BTU or Calories to temperature (°F or °C) so you have to use the Cp that goes with the measurement system you are using. For a particular formula (say a 60% hydration bagel dough) and a particular flour and a particular mixer and a particular DDT, you can find (by trial and success) a relationship between flour temperature and water temperature that delivers the desired dough temperature.

If you change the desired dough temperature by a little bit (a couple of degrees) the formula will work fine, but if you get too far away from the calibration point it will give you bad values. So yes, the computers that measure all of the inputs will give you reliable results, but if you want to do it for yourself you have to establish a baseline formula and calibrate your mixer. If you are making the same thing day after day it will work fine. If you are making different stuff every day then you will have to back to the physics and still keep good records.

I have created a one page explanation that attempts to develop the quantitative calculation of Friction Factor from basic principles. I have included below a .jpg image instead of the text since this site doesn't support any of the required equation formatting.

The 'one page explanation' link on Dropbox has been deleted. Is it shown elsewhere?

Thank you @anton for pointing this out. The link was in fact dead (too old for bitly to maintain), so I have pasted a .jpg version into the original post which seems to work just fine. I will have to remember this the next time tfl mangles a text string.