Incorrect "DME Required" in Yeast Starter calculator?

[Elemental Brews]

Hi Folks,

I was playing around with the yeast pitch rate and starter calculator, when I noticed the DME numbers seem... more than a little off. When told to calculate for 1L of starter at 1.036 gravity, it suggests using 3.6oz / 102.7g of DME. Perhaps I'm simply misinformed, but as I understand things, that can't be correct.

The gravity of a liquid is the weight of the liquid divided by the weight of an equal volume of pure water (https://en.wikipedia.org/wiki/Gravity_(alcoholic_beverage)#Specific_gravity). 1L of water is ~1000g, with some variation due to temperature. To get a gravity of 1.036, you therefore need liquid weighing 1036g per liter, which in this case means dissolving 36g DME into 1L (1000g) of water -- not 3.6oz DME, which is nearly 3x as much!

Fiddling with the calculator, this error seems pretty consistent. Change the desired gravity to 1.040, and the calculator suggests 4.0oz. Change it to 1.012, and it suggests 1.2oz. Double the starter volume, and it doubles the suggested DME. But it all seems to be based on an initially faulty calculation, at least as far as my understanding of the basic formula indicates.

Now, with all that said, before posting this, I looked around and found a couple other online yeast starter calculators to check against. One of them seems to get the exact same results as the Brewer's Friend calculator (within sigfig rounding); oddly, the other gets results that are lower by about 5%. Neither comes anywhere close to what I calculate.

So what's going on? How can you dissolve 102.7g DME into 1L of water and get a gravity of 1.036? Am I missing some crucial detail about how this should be calculated? The calculation is extremely straightforward from the definition of gravity, so I'm not sure what I could be doing wrong. On the other hand, since the other calculators seem to more-or-less agree with Brewer's Friend (and disagree with me), I have to second-guess myself.

I'm making a starter tomorrow, so I'm somewhat inclined to break out the hydrometer and test it before I inoculate it with yeast. But either way, I want to understand where the Brewer's Friend calculation comes from.

Thanks!

 

[Myndflyte]

People may correct me if I'm wrong because I don't know for sure, but my guess is that 1g of DME in a liter of water isn't going to change the gravity to 1.001. DME isn't straight sugar, and I don't even know if sugar would change it that way either. Think of any other solid. Adding 10g of salt isn't going to change the gravity the way you calculated and because there are other things in DME, it won't either.

Pretty much the rule of thumb for a starter is 100g DME in 1L of water will get you around 1.038.

 

[Elemental Brews]

That could be essentially what's happening, if folks are being less-than-accurate with the term "gravity" in the context of starters. Technically, adding 10g of salt would change the gravity just as much as 10g of sucrose or 10g of maltose (I repeat: unless I'm getting something horribly wrong). Any equal mass of solid that is 100% dissolved into the liquid should have the exact same effect on gravity, as a hydrometer would measure it. The hydrometer doesn't know whether the liquid has DME or table sugar or salt dissolved in it.

It is possible though, that the "gravity" mentioned in started advice is really gravity-due-to-sugar or something like that, and in that case yes it is possible using 10-to-1 water to DME by weight would yield 1.036 of this other version of gravity. The overall gravity would be 1.100 as I calculate, but the gravity-due-to-sugar would be different, and calculating it would depend on knowing what percent of the mass of DME is actually sugar or whatever. I hadn't considered this possibility.

I have noticed previously that the rule of thumb is 10-to-1 ratio of water to DME by weight for starters. I just thought they were wrong at the time, and I didn't want to muddy the waters of my question by bringing that up. It's only now I noticed the calculators agree with this widespread advice.

There are 3 main possibilities here, considering what you've suggested:

1. I'm horribly wrong somehow, and 100g of DME in 1L of water results in 1.036 gravity. My test with the hydrometer later today should tell me whether this is the case.
2. I'm correct that the actual gravity which results from this 10-to-1 advice will be 1.100, not 1.036 (as measurable by a hydrometer) -- however the 1.038 number doesn't refer to overall gravity, it refers to gravity-due-to-sugar or something. If so, that's great, and someone should write a magazine article or blog post explaining this for the benefit of OCD mathy-science-types like me.
3. Or, it could turn out that the emperor has no clothes, and someone's incorrect calculation from years and years ago has spread throughout the homebrewing community to the point of becoming ubiquitous. That would be rather interesting to discover. Then my question would be: has everyone been making substandard 1.100-gravity starters all this time when 1.030-1.040 is the goal, or is 1.100 actually the gravity to shoot for and we should simply stop claiming that 10-to-1 somehow makes 1.036?

So... where does the Brewer's Friend calculation come from?

 

[Ozarks Mountain Brewery]

the equation is not set in stone, by the way hydrometers don't care if its sugar or not they measure total ppm of solids vs water, it can be 1-2 to 1-1.5, I don't really measure any more as long as your yeast have enough room to replicate without stressing too much, too much room and not enough sugar they get lazy, not enough room and they get stressed and possible cause an off flavor so over the years thieve just by trial and error come up with a safe range but again it’s not a set in stone formula, yeast are a living cell and just like humans not all are the same

 

[Elemental Brews]

I just measured experimentally, and it seems that 10-to-1 ratio of water to DME by weight really does make around 1.040 gravity as measured by a hydrometer (could be closer to the calculator's 1.036 in reality, there's plenty of room for error in my process). So, it appears I'm just plain wrong.

My question remains, WHY? How is my basic math, derived from the definition of specific gravity, so far off? I'm not just asking so I can use the "right" amount of DME in my starter, I want to understand. I realize at this point, this isn't really the ideal forum for this question, since it no longer has anything to do with using the Recipe Editor. All the same, I would really appreciate if someone could explain this to me.