# Calculation of IBU additions after flame out (no chill/whirlpool)



## RelaxedBrewer (4/7/14)

After a fair bit of reading and playing around I have done some work on how to calculate IBUs after flame out.

Attached is an article outlining what I have done.

Hopefully some of you actually read it and can offer some thoughts.

If anyone has any questions I am happy to answer them. 

View attachment nochillwhirlpoolIBUutilizationcalculation1.pdf


----------



## RelaxedBrewer (4/7/14)

I forgot to point out that the article is just first draft.


----------



## Not For Horses (4/7/14)

I had a read through it. Seems like the maths is pretty solid although it has been a few years since I studied differential calculus.
The numbers seem to follow accepted wisdom which, from what I can gather, is based on empirical evidence.


----------



## Alex.Tas (9/7/14)

Thats awesome. Great work, love the application of science and maths! the difference between the lid on and lid off method was far grater than i expected. I reckon the extraction fan was the main culprit, drawing air over the top of your cooling wort.
Thanks heaps for doing this investigation. taking 5 minute readings for 2 hours must have been a pain!


----------



## AndrewQLD (9/7/14)

Very interesting read, I would worry about cubing when the temp drops down to 80 c as you will get a further drop in temp on transfer and could run the risk of infection.


----------



## RelaxedBrewer (9/7/14)

AndrewQLD said:


> Very interesting read, I would worry about cubing when the temp drops down to 80 c as you will get a further drop in temp on transfer and could run the risk of infection.


Yeah, I actually brewed yesterday and began the transfer from the kettle to the cube after 22 min of cooling with the lid off. The temperature was still 85C (According to my equation it should have been 86C, so pretty close). I would not recommend transferring at 80C either. I will make my article clearer.




Alex.Tas said:


> Thats awesome. Great work, love the application of science and maths! the difference between the lid on and lid off method was far grater than i expected. I reckon the extraction fan was the main culprit, drawing air over the top of your cooling wort.
> Thanks heaps for doing this investigation. taking 5 minute readings for 2 hours must have been a pain!


Thanks mate, much appreciated. I reckon you are right about the extractor fan. 
The 5 min readings were a pain in the ass, but I had a few brews to help and managed to write a fair chunk of the article during it.


----------



## /// (9/7/14)

The usual software programs used to pretty much ignore the BU's gained from the whirlpool step, so the no-chill isomerisation rates would be out of the picture.

i know what i usually get for the whirlpool step thru testing with a photospectrometer via a pentance absorbance test, it can be up to 80% depending on the amount of BU needed, the gravity and the amount of whirlpool hop added. In our lager we use no bittering hop, and just about to drop out the bittering hop for the ligher golden ale.

My advise to no chill brewers is to remove any 'mid' additions, ie. hops at 15, 10, 5 minutes, and just utilise the whirlpool with a standard amount taken from the step.

Not sure if I would drop the temp and then fill the no-chill container, i would go as hot as possible to maximise the pasteurization units particularly if you are reusing the container.


----------



## RelaxedBrewer (9/7/14)

/// said:


> The usual software programs used to pretty much ignore the BU's gained from the whirlpool step, so the no-chill isomerisation rates would be out of the picture.
> 
> i know what i usually get for the whirlpool step thru testing with a photospectrometer via a pentance absorbance test, it can be up to 80% depending on the amount of BU needed, the gravity and the amount of whirlpool hop added. In our lager we use no bittering hop, and just about to drop out the bittering hop for the ligher golden ale.
> 
> ...


You get a utilization of 80%? Or 80% of your IBUs are coming form the whirlpool (I think you must mean the latter).

If you have some actual numbers on IBUs you get from whirlpool with time and temp I would love to see them.


----------



## /// (9/7/14)

Sorry, i get 80% of the BU's from the whirlpool.

I'll do more testing in a few weeks, but i know from practice;

* Pale ale with 3 grams a litre of whirlpool gives 50% of total BU from whirlpool (mix of mid - low alpha hops)
* IPA with 5 gms a litre whirlpool gives 50% of total BU (using a mix of mid to medium high alpha US hops)
* Golden Ale with 2.5 gms a litre whirlpool gives 80% (using high alpha Aussie hops)

Some of the Aussie hops have alphas into the medium to high teens, so this has a massive impact, as does your gravity. And it is approxmiates as well ... as I said, need to test again.


----------



## Online Brewing Supplies (9/7/14)

How long are you w/pooling for before reaching ferment temps and what temp is the initial w/pool ?
Nev


----------



## RelaxedBrewer (9/7/14)

/// said:


> Sorry, i get 80% of the BU's from the whirlpool.
> 
> I'll do more testing in a few weeks, but i know from practice;
> 
> ...



I think you might have missed the point of my article.

I have derived an equation that will let you estimate how many IBUs you will get from your hop additions after flameout (if you know how your system cools) by giving a utilisation for the hop addition. (utilisation is how much of the alpha acids we add to the beer/wort actually ends up as iso-alpha acids for the addition)


If you had understood this, my apologies.


----------



## Lord Raja Goomba I (9/7/14)

I've been thinking about whether transferring at high temps into cube but waiting until the cube has cooled to 90 (or 80 or whatever) degrees to cube hop, in order to replicate a shorter isomerisation time (say of a 5 minute chilled addition).

This might help figure that out.


----------



## technobabble66 (9/7/14)

Hey RB, Great work - totally agree with the hand wavy thing.
Great to see a little science/math to back-up the various suggested estimates. Also good to see the important differentiation of lid on & off!

One minor detail wrt the Area under the Curve graph near the end, and the subsequent U values from it (page 7): i assume the t on the x-axis is for time in minutes, or is it still in seconds (100's)?
And the values for U for Lid On/Off are calculated for what value of t? 25mins?

FWIW, i did a fair bit of reading ~12mo's ago to get a handle on this whirlpool IBU stuff.
Got similarly annoyed by the vagueness of something that seemed vitally important (cf the extremes people went to to justify the whole rehydration debate <_< ).
I eventually found the repeated statements (from some respected/experienced brewers) around the idea of a 20min whirlpool equating to an extra 12mins of boil time, and cubing was the equivalent of an extra 20mins boil time. (so i guess if you whirlpool & cube, the extra 30-35mins calculated gets you a fair way to the 60min equivalent your calculation indicate). As III above stated, it was suggested this varied a fair bit for the higher %AA hops. Sorry, no links to the threads/papers i read to back this hand wavy opinion, though.

PS: the brew i did on the weekend (for the Swap) was a small 20min addition with a rather large Flameout addition (cascade + Nelson), followed by 45mins stand with the lid off and a fan blowing on it to drop the temp. (coincidently i think i checked the temp when i started draining & it was something like 72°C ?). I estimated this as a ~24mins boil equivalent (2x 12mins for a 20min stand + a 20min whirlpool). So it'll be interesting to see how the IBU's appear when it comes to drinking time.


----------



## TheWiggman (9/7/14)

Posting in epic thread.

Top work relaxedbrewer, I take it you're not a forkilft driver? And if you are, more credit to you.

What would be unreal is if this simulation could be tested in real life to see how closely the measured bitterness lines up with the calculated bitterness. If the two are close then you could put that calculator on a web page and be guaranteed lots of hits from home brewers around the world. It's certainly making me think about my next approach as a no-chiller with limited batches.

One question I have surrounds the utilisation as a figure in the document. What do the actual utilisation percentages mean in terms of IBU? For example, if I'm targeting 30 IBU and I have a calulated 60 min addition and 5 mins that ends up being 30 for a chilled batch, what do I do to adjust this so that I can acheive the same thing when no-chilling?

ED: More clearly I suppose what I'm trying to say is how would I correlate utilisation with IBU? 5% AA hops x 30% calculated utilisation = ????
ED again - http://www.howtobrew.com/section1/chapter5-5.html should tide me over to the above query. Though it would be nice to include it in your next version of the doc 
Also please say 'maths' and not 'math', 'cause I'm 'Strayan.


----------



## RelaxedBrewer (9/7/14)

I have done a little more work and a test brew.
Since there seems to be some interest generating I will probably post a 2nd draft in a couple of days that will include some examples of what to expect for different systems as well as my own and a bit of a tidy up.




technobabble66 said:


> One minor detail wrt the Area under the Curve graph near the end, and the subsequent U values from it (page 7): i assume the t on the x-axis is for time in minutes, or is it still in seconds (100's)?
> And the values for U for Lid On/Off are calculated for what value of t? 25mins?


I am at work at the moment and all my data is at home so will have to check to be 100% sure. 
The time is in minutes on the Area under the curve graph. It also looks like the heading should have been for lid off.
U was calculated over 2.5 hrs form memory but would have to check.




TheWiggman said:


> What would be unreal is if this simulation could be tested in real life to see how closely the measured bitterness lines up with the calculated bitterness. If the two are close then you could put that calculator on a web page and be guaranteed lots of hits from home brewers around the world. It's certainly making me think about my next approach as a no-chiller with limited batches.


I would love to do this. If /// gets back to me with some details it might be possible.
I have also been considering contacting someone from one of the Universities that does food science related research and seeing if they are interested.




TheWiggman said:


> One question I have surrounds the utilisation as a figure in the document. What do the actual utilisation percentages mean in terms of IBU? For example, if I'm targeting 30 IBU and I have a calulated 60 min addition and 5 mins that ends up being 30 for a chilled batch, what do I do to adjust this so that I can acheive the same thing when no-chilling?
> 
> ED: More clearly I suppose what I'm trying to say is how would I correlate utilisation with IBU? 5% AA hops x 30% calculated utilisation = ????
> ED again - http://www.howtobrew.com/section1/chapter5-5.html should tide me over to the above query. Though it would be nice to include it in your next version of the doc
> Also please say 'maths' and not 'math', 'cause I'm 'Strayan.


The brewing software I use lets me add whirlpool hop additions (I assume most do). These whirlpool additions require a utilisation to be entered. The utilisation calculated can be entered into this to give the IBUs.
eg Using my method a flame out whirlpool addition on my system has a U = 13.6%. If we used some high AA hops like 14% AA Galaxy, to get and IBU of 30 from the addition we would need to add ~38g of hops. Does that make sense?
PS. I will correct math to maths for you


----------



## RelaxedBrewer (9/7/14)

Lord Raja Goomba I said:


> I've been thinking about whether transferring at high temps into cube but waiting until the cube has cooled to 90 (or 80 or whatever) degrees to cube hop, in order to replicate a shorter isomerisation time (say of a 5 minute chilled addition).
> 
> This might help figure that out.


I have been doing something similar and is what triggered this bit of work for me. This should be prefect for what you are doing.


----------



## Lord Raja Goomba I (9/7/14)

RelaxedBrewer said:


> I have been doing something similar and is what triggered this bit of work for me. This should be prefect for what you are doing.


I suppose you assume the 'lid on' calculations to be about right for cube hopping and immediately transferring and then waiting?


----------



## RelaxedBrewer (9/7/14)

Lord Raja Goomba I said:


> I suppose you assume the 'lid on' calculations to be about right for cube hopping and immediately transferring and then waiting?


I did a brew the other day and did.
However, I found that my cube was cooling slightly faster than the 'lid on' did. I think it is because after fill and seal the cube I put it on the concrete floor of my garage. This probably draws a fair bit of the heat out to the floor. I had planned on adding an addition at 75C but it was down to 66C. I am going to have to redo the cooling experiment with my cube and update the article.

I plan on doing something like lid off cooling to 90C (~15min), then fill the cube and cube chill. With this I can have a hop addition at flameout and at 90C easily (and others in between). 
There is always the possibility of opening the cube for more additions later but this adds the risk of infection and I only do it if pitching the next day (others will say don't do it at all).


----------



## Trevandjo (9/7/14)

RelaxedBrewer said:


> After a fair bit of reading and playing around I have done some work on how to calculate IBUs after flame out.
> 
> Attached is an article outlining what I have done.
> 
> ...


I took the option of skipping the maths sections. I did get a bit overwhelmed with some of it. 

Great work with the research. I'm soon to begin no chilling so would certainly find a calculator useful. 

Thanks
Trev


----------



## /// (9/7/14)

RelaxedBrewer said:


> If you had understood this, my apologies.


Hi - I got that. More so my point is that you can get a heap of utilisation, perhaps more with the difference in cooling times.

This is good stuff to look at, particularly as it relates directly to the brewers here


----------



## lael (10/7/14)

Scotty,how long are you whirlpooling / having hop and wort contact to see those utilisation rates?


----------



## Midnight Brew (10/7/14)

Just to throw in some discussion, I currently calculate my cube hop addition as a 20 minute boil addition.

I've measure my wort 20 minutes after flameout with lid on and got 97C. Then I whirlpooled and waited 40 minutes with the lid on and got 95C. That is what I base my guesstimates at. Having a read of your article RB I'm now thinking I havnt measured my wort after transfer to the cube and Im going to say there would be a few additional degrees lost in that transfer itself, so I could realistically have wort at 90 - > 95C. (I'll measure this heat loss next brew)

Had a quick browse at the beersmith software and the default steep utilisation is 50% assuming that the wort is at the default temperature of 90C (at least 90C is recommended).

Went back and had a play with a few recipes already brewed and its literally half of what I have been estimating at. In one example its gone from 14IBU at cube hop to 7IBU. Now Im not sure whether I could detect 7IBU difference unless that samples were side by side. Sure does make for an interesting formulation of how we design our beers. Id love to be able to actually measure the IBU in a beer.


----------



## /// (10/7/14)

Whirlpool for 10, sit for 5, then run off in 45.

For the high alpha Aussie hops, they fry off really quick. Hence why we dry hop alot and hold right back on the bittering. I am also lucky that with the colandria it helps to manage the boil, remember hops help to reduce boil overs.


----------



## technobabble66 (10/7/14)

Hey III, apologies for being a bit of a thicker, but just to clarify, are you saying it takes you 45mins to drain your kettle?


----------



## jyo (10/7/14)

/// is a commercial brewer, mate. He's talking 1000's of litres 

This is great discussion. Top work, relaxedbrewer. With APA / IPA and high alpha hops I've learned the hard way (and from reading ///'s posts in the past about this) to be more aware of the bittering contributions of whirlpool hops. It will be cool to have a simple formula to help calculate.

Cheers.


----------



## /// (10/7/14)

Yep sorry, on average we have about 2100l in the whirlpool, but follow the same principles at home. Also one year made about 30000l of wort packs for another business and followed the same principles.


----------



## pat86 (13/7/14)

Very interesting, thanks OP. Scotty if you or the YH guys made fresh wort, they would definitely be the first fresh wort kits I would want to buy!


----------



## RelaxedBrewer (18/7/14)

OK, I have done a second draft of the article.
I have included an example brew I did and some example utilisations from different chilling techniques. I also cleaned a few things up.

I understand that this article may go over some peoples heads (most people are not going to understand the maths, I know it took me a little while to get my head around at first). So if you don't want to read the article I will summarise it.
In summary;
1) I have derived an equation that can be used to estimate alpha acid utilisation and therefore IBUs with changing temperatures.
2) This can be used for estimating IBUs from whirlpool/hop stand and no chill additions.
3) This work was an extension of some other peoples work published in per reviewed scientific journals.
4) I have given examples of my no chill technique and the utilisations I expect on my system for different hop additions after flame out.
5) I applied this technique to a big hoppy West Coast IPA style recipe and showed the IBUs I expected from each hop addition.
6) I also have given some examples of utilisations from a few other techniques/systems.
7) I don't have access to equipment to test for alpha acids and there can not get actual IBU values. I am probably going to try to contact a university and see if anyone is interested in this work and try to check with real world values. If this happens we would most likely produce a proper scientific paper. 

View attachment nochillwhirlpoolIBUutilizationcalculation-3.pdf


----------



## danestead (18/7/14)

RelaxedBrewer said:


> OK, I have done a second draft of the article.
> I have included an example brew I did and some example utilisations from different chilling techniques. I also cleaned a few things up.
> 
> I understand that this article may go over some peoples heads (most people are not going to understand the maths, I know it took me a little while to get my head around at first). So if you don't want to read the article I will summarise it.
> ...


That is really bloody awesome that you have gone to the effort of doing the research and experimentation and summaried your findings. It seems it has been a big unknown - until maybe now!

I used to think I was reasonable considering I did double maths at school however the equations are getting a little confusing to me. I've worked on a couple of rules of thumb that I've read online for isomerisation at temperatures other than 100c so it'd be great if I could compare those rules to your equations answers.

It looks like in your paper that the utilisation of hops varies with the gravity of the wort. This was always considered the case I believe however John Palmer has changed his thoughts on that and has written somewhere (maybe an updated 'How to Brew' book - I'm not sure) that there is no evidence that this happens. It'd be interesting to hear your thoughts on that and maybe if you have the equipment to test IBU's, you could test a few different wort gravities vs utilisation. Anyway that is slightly off topic.

What I'm asking is, are you able to show me how I use your equation to calculate how many IBU's I will extract for the following 2 situations.

I have used Promash to calculate a 15min addition and the calculated IBU's.

1.050 OG wort
20g of Citra (10% AA) for 15mins
(Note: I'm not sure what the_ iso-a-acidt vs a-acid0_ is but if it refers to the degradation of the AA% of hops over time in storage, lets say that the Citra was 12% AA to begin with and has been stored for a while in the freezer to end up at 10% AA now)

Promash gives me 22.5 IBU's based on Tinseth and a boil addition (100c)
My rule of thumb is that at 90c you halve the IBU's as compared to a 100c addition and that at 75c it is about 10-15% of the 100c amount, therefore:

@ 90c for 15min I estimate 11.25 IBU's
@ 75c for 15min I estimate 2.25-3.375 IBU's


How does your equation compare and can you show your working so I can later do it myself. Lets assume the temp is kept constant at 90 and 75 deg.

Cheers.


----------



## RelaxedBrewer (18/7/14)

@danestead I will run though it for you after the weekend (I have a rather big one with the VIC case swap).

Your rule of thumb seems like a pretty good estimate though.


----------



## RelaxedBrewer (23/7/14)

danestead said:


> @ 90c for 15min I estimate 11.25 IBU's
> @ 75c for 15min I estimate 2.25-3.375 IBU's
> 
> How does your equation compare and can you show your working so I can later do it myself. Lets assume the temp is kept constant at 90 and 75 deg.


In the situation you are proposing we are holding the temperature constant and you do not even need most of the work I have done. I have made equations that will work with changing temperatures something that other have not done yet (as far as I am aware).

So for your case we can use existing formula.
To get utilisation we use
U = 1- e^(-kt) (equation 2 in my article).
and k is temperature dependent
k = Ae^(-E/RT) (equation 2 in my article).
The constants A and E/R were solved by experimentation in the second paper I listed (JASKULA, B. KAFARSKI, P AERTS,G. COOMAN, L. A Kinetic Study on the Isomerization of Hop r-Acids J. Agric. Food Chem. 2008, 56, 6408–6415)
and were found to be A=3.13*109 and E/R=11661.

So for your situation all you need to do is plug in the temperature (T), A and E/R into the equation for k.(note: T is in Kelvin)
Then once you have k plug that into the utilisation equation with the time and find U (note t is in seconds).

So for 15 min @ 90C we get U = 7.2% 
This equates to an IBU of 8.

and for 15 min @ 75C we get U = 0.8%
This equates to an IBU of 0.8

So your estimates are higher than mine.
I have never used promash, does it give utilisations for hop additions as well as IBUs? The brewing software I have gives 13 IBUs and a 12 U for a 15 min boil (100C) addition of 10AA Citra in 50 OG wort. This is a lot different from what you say Promash is giving you (22.5 IBU). What batch size are you doing and what boil size? (The number I quoted above are for 19L with a 23L pre boil volume)


(The interesting thing that I have done is modify this above method to work with a changing temperature by using some calculus and time series estimations)


----------



## danestead (23/7/14)

Thanks for such a detailed post!

Im on holidays so dont have promash infront of me however im pretty sure it only gives an IBU number. Whilst we are talking about utilisation, when you say that in my 90 degree example there is 7.2% utilisation, to get 8 IBU's are you just rounding up or is the utilisation multiplied by the hop AA%?

The batch size I was using was 25L however that is actually my post-boil volume. I always use my post boil volume as batch size and use my efficiency as a mash efficiency. I manually calculate my losses rather than calling my batch 21L (volume into fermenter) and inputting my losses to kettle, trub, shrinkage into the software for it to calculate it all automatically. Preboil volume on my 25L 'batch' would usually be 28.1L for a 60min boil.


----------



## Forever Wort (30/7/14)

I heard about this article at the Merri Mashers meeting last night. This is valuable and great work Kris.

For the less mathematically-minded among us brewers, all I can say is keep at it and hopefully we will one day see an accurate software calculator that will be able to give us estimated no-chill IBU additions based on simple variables we can input ourselves (gravity, AA, cooling times).


----------



## verysupple (30/7/14)

RelaxedBrewer said:


> In the situation you are proposing we are holding the temperature constant and you do not even need most of the work I have done. I have made equations that will work with changing temperatures something that other have not done yet (as far as I am aware).
> 
> So for your case we can use existing formula.
> To get utilisation we use
> ...


I've been playing around with this and I think you may have made a mistake.

For 15 min at 90 C. I get U = 3.1 % (which matches Table 2 in Jaskula et al, you got 7.2 %) and for 15 min at 75 C I get U = 0.8 % (the same as you).

Other than that, great find!


----------



## technobabble66 (30/7/14)

RelaxedBrewer said:


> ...
> 
> So for 15 min @ 90C we get U = 7.2%
> This equates to an IBU of 8.
> ...


Might need to check this Kris. I think for 90mins, U = 3.1%

Edit - curses for not refreshing my page, very supple beat me to it!

Again - Great paper!
We (ie: you  ) just need to organise a quick little spreadsheet where a brewer can do a quick few temp checks, get a rough estimate of the cooling rate for their kettle/cube, then plug in a time to get a whirlpool/cube Utilisation estimate; and hence by-pass having to do the calculations themselves.

Edit 2: I think Kris used 100°C in his calc's instead of 90°C. No biggie.


----------



## RelaxedBrewer (30/7/14)

Yeah.. sorry I sorted that stuff out via PMs. I accidentally listed the 100C calculation as the 90C, I should have updated the post.

A quick update: I spoke to a professor from RMIT alst week. He is quite interested in this kind of work. He is busy with other work for the next month or so but was pretty keen to collaborate with me after. This means I should be able to take some measurements and check the formula against real world data some time in the near future.


----------



## Byran (30/7/14)

/// said:


> My advise to no chill brewers is to remove any 'mid' additions, ie. hops at 15, 10, 5 minutes, and just utilise the whirlpool with a standard amount taken from the step.
> 
> Not sure if I would drop the temp and then fill the no-chill container, i would go as hot as possible to maximise the pasteurization units particularly if you are reusing the container.


After much experimentation with no chill I have basically ended up in this exact scenario. On some lighter beers I only do a whirlpool addition. It feels weird to not boil any hops but it works.


----------



## tateg (28/10/14)

Hi Guys
I am just trying to work the above equations out of curiosity but cant seem to get it going.
for the below scenario can someone tell me the actual equation using the data

So for 15 min @ 90C we get U = 7.2% 
This equates to an IBU of 8.

U = 1- e^(-kt) (equation 2 in my article).
and k is temperature dependent
k = Ae^(-E/RT) (equation 2 in my article).

I understand what the values mean just not sure about how to enter them 

thanks


----------



## danestead (28/10/14)

tateg said:


> Hi Guys
> I am just trying to work the above equations out of curiosity but cant seem to get it going.
> for the below scenario can someone tell me the actual equation using the data
> 
> ...


Try PM relaxedbrewer. He originally had some small typos to the formulas he wrote up however will be able to help you out via PM to sort out your problem.


----------

