Hop Math!

[JGriff731]

Ok, so the recipe is for a Samuel Smith's Winter Welcome clone as found in "Clone Brews". The extract recipe calls for 1.5oz. of EKG's @ 4.2 AA which is 6.4 HBU's. I know how to calculate the HBU's, amount of hops time's the AA=HBU. HOWEVER, the all grain recipe call's for 4.5 HBU's of EKG for bittering, which is 30% less. I'm not much of a math wizz, soooo, I need some help here. Do I reduce the amount of hops that go in? Or, do I reduce the AA to achieve the proper HBU?

Thanks,
Justin

 

[jtd_419]

They are saying to adjust the weight by thirty percent to change hbu...

 

[jtd_419]

1.05 oz or 30g would be the weight your looking for

 

[WoodlandBrew]

Can you post a link to the recipe. Are the boil times different? If it is 30% lower by weight with the same boil time then maintain the HBU by scaling the weight based the AA of your hops.

 

[ACbrewer]

Is it possible that the extract brew calls for a reduced boil amount? There is thought to be (and debate about) the amount of hop oil going into solution being dependant on boil size and gravity of solution at time of boil (ie a partial boil has about 2x the relative gravity of a full boil). By increasing the amount of hops in a partial boil, this allows for more hop oil to be put into solution.

 

[JGriff731]

The boil times are different, just took a second look. The boil time for the extract is 45min. and the all grain is 90min. I just brought this up as it was vague in how to get to the adjusted HBU's for the all grain, actually it doesn't even mention how in the book anywhere. As said before the extract calls for 1.5oz of EKG @ 4.2AA equaling 6.4 HBU and does not say to adjust weight nor AA in the all grain instructions. I do appreciate the info. Will more than likely stick with taking 30% off the of weight.

 

[WoodlandBrew]

Adjusting weight based on AA to match HBU is just standard operating procedure. As for the adjusted amounts for boil time that sounds about right. Utilization is also dependant on boil volume and sugar concentration of the wort.

 

[ACbrewer]

I just brought this up as it was vague in how to get to the adjusted HBU's for the all grain, actually it doesn't even mention how in the book anywhere.
I do appreciate the info. Will more than likely stick with taking 30% off the of weight.

I've seen nothing hard and fast for the conversion on hop usage. I've even seen disagreement that it is needed for the 3 things mentioned (boil time, volume, gravity of boil). Making matters worse, it also seems to be non linear on all 3 counts.

And as I said before, there are disputes on does any of it matter or not, and how much. I think all 3 do, but have no emperical evidence to point to.

 

[ajdelange]

You are confusing the essential oils which are responsible for the flavors and aromas of hops with the resins which are responsible for the bitterness. The oils are volatile and fly off during extended boils which is why flavor and aroma hops charges are loaded close to knockout. Time is really the main thing to consider with respect to the oils - the longer the boil the less aroma/flavor (with first wort hopping being somewhat mysterious in this regard).

The resins are not soluble. For them to go into solution they must be isomerized and this takes place during the boil. The longer the boil, the more resins (acids) are isomerized and go into solution so the longer the boil the more bitterness. pH is also a factor. The higher the pH the more bitterness is extracted. The higher the gravity of the wort the less isomerization and dissolution. Thus the following all effect the amount of bitterness extracted from a hop charge:
1. Weight of the charge
2. AA percentage
3. Time of boil
4. pH
5. Gravity of wort.

One can trade these off. For example a short boil with a high alpha hop will give the same bitterness as a longer boil with a lower alpha hop (and retain more of the oils as well). There are various formulas which attempt to model the amount of bitterness one gets from a particular length of boil from a particular hop charge. The one that probably does the best job in the majority of cases is the Tinseth formula:

utilization% = 100*((1 - exp(-0.04*minutes))/4.15)*(1.65*0.000125^(SG-1))

but even it leaves something to be desired and that is because, among other things, what it says on the hops package is not necessarily the actual AA content of the hops therein. Alpha acids lose potency dependent on storage conditions. The longer from harvest the lower the AA. High temperature and exposure to oxygen accelerate the loss.

The following graph shows the errors i.e. the difference between what the Tinseth model predicted and the measured IBU levels of 23 beers.

 

[ncbrewer]

The higher the gravity of the wort the less isomerization and dissolution.

Your comments about higher wort gravity relating to lower isomerization and dissolution are very interesting. For the last several years, there has been some serious debate about this correlation – some thought that the break material is the direct cause of the reduction in hop utilization. Does your comment mean the issue has been resolved?

 

[ajdelange]

No, not as far as I know. I'm not sure I even believe it. Certainly the data I posted don't show it.

 

[jmf143]

The one that probably does the best job in the majority of cases is the Tinseth formula:

utilization% = 100*((1 - exp(-0.04*minutes))/4.15)*(1.65*0.000125^(SG-1))

AJ, what does "exp" refer to? What would the utilization be for a 60 minute addition into 1.050 wort?

 

[WoodlandBrew]

Exp is exponential
e to the power of x
e^x
2.718281828459^x

Would be other ways of writing it.

For the scenario you described utilization would be 23%. Google "Tinseth calculator" to play with the equation.

 

[ajdelange]

If you have Excel (and most people seem to) type 60 into cell A1 and 1.05 into cell A2. Then copy the formula from the post including the equals sign but not including the "utilization%" and paste it into cell A3. Now edit that cell replacing 'minutes' with A1 and 'SG' with A2. Press return and cell A3 will show the utilization: 23.066%. You can then put in any values for time and SG you want to obtain other values.

exp refers to the 'exponential function': e^x = 1 + x/1 + x^2/(1*2) + x^3/(1*2*3)+ x^4/(1*2*3*4) + ... x^n/n!

e is Euler's (Swiss mathematician) number (not Euler's constant), hence the symbol e. Many things in nature follow the exponential function and e appears in lots and lots of places in engineering, math and science. The important thing here is that the hops utilization as a function of time 'fits' the exponential law. The practical significance is that if you type '=exp(A1)' in a spreadsheet the spreadsheet will calculate the value of the exponential for the argument in cell A1.

 

[ACbrewer]

Wouldn't you then after taking the formula get a utilzation % but not a bitterness effect on the wort? I mean you'd have to adjust it by the AA% or something to get the IBU/HBU or whatever for the beer?

 

[ajdelange]

Wouldn't you then after taking the formula get a utilzation % but not a bitterness effect on the wort? I mean you'd have to adjust it by the AA% or something to get the IBU/HBU or whatever for the beer?

Yes. You multiply the weight of the hop charge, in grams, by AA%/100 and divide by the number of liters of beer. This gives you the grams of alpha acids per liter. Multiply by 1000 to get mg and then by the utilization percentage /100 to get the mg/L isomerized alpha acids.

To quote the ASBC Methods of Analysis:

"Reports of the Subcommittee on Determination of Isohumulones in Beer for 1967 and 1968 (Ref. 1) indicate that bitterness units (BU), as determined in Method A below, express the bitter flavor of beer satisfactorily,..."

Method A measures the mg/L isohumulone in the beer.

 

[jmf143]

Does Tinseth's formula break down at the edges i.e wort SG above or below a specified amount or boil times longer or shorter than a specified time? I'd like to incorporate it into a recipe formulation worksheet I'm building if its robust enough.

 

[WoodlandBrew]

I've been using the equation in my spread sheet for years. It hasn't given me any garbage unless I put garbage it. Works just dandy at estimating bitterness. It's not going to give you an accurate representation of aroma hops or dry hops, but the bittness value has always seemed useful to me.

 

[ajdelange]

Does Tinseth's formula break down at the edges i.e wort SG above or below a specified amount or boil times longer or shorter than a specified time? I'd like to incorporate it into a recipe formulation worksheet I'm building if its robust enough.

Can't say. The graph I posted in #9 represents the extent of beers over which I have checked it. I wouldn't say that graph represents sterling performance by any means but at least the errors seem more or less random so I think we can conclude that it at least models the trends. It is a model and all models have their weaknesses.