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Barrel Surface Area to Volume Ratio, Bourbon and Wine

Posted: Sat Nov 04, 2017 4:48 pm
by Badmotivator
Barrel Surface Area to Volume (SA/V) Measurements

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I have had a miserable time trying to get reliable measurements for surface area to volume ratios in large barrels. I’m going to name some of the problems and discuss solutions to them. I include some measurements here and hope to help others avoid some of the frustrations I have had trying to pin down the numbers.
  • Problems with finding SA/V measurements:
  • Very few people are interested in precise measurements of interior SA/V, so very little is written about it. Much of the writing you do find is about generalities (i.e. “Small barrels have a higher SA/V so your spirit will age faster ha ha”) and are not helpful.
  • There are a few websites with charts showing interior surface area of a range of barrel sizes, for example from Deep South Barrels, Red Head Barrels, Tall Ship Barrels, et. al, but upon inspection their numbers are insane. To give you some idea of how insane they are… to match their claim that the SA for a 53 gallon barrel is 6535 in2, a cylinder would have to have a 3.8” radius and be 22.5 feet long. This is a real issue, because these numbers are readily available, easily found by a Google search, and dangerously incorrect. If you were to follow their numbers, you may damage your spirits. Let's say this again, but in bold: Deep South Barrels and Red Head Barrels surface area to volume charts are wrong. Don't use their numbers for anything.
  • Barrels come in many different volumes and geometries. Bourbon barrels are reasonably standardized, but many spirits are aged in hogsheads, butts, barriques, etc. If you are looking to match the characteristics of the spirit you like, it will be tough to get measurements of the surface area to volume ratio that is appropriate for you to aim for.
  • The real-world geometry of a cask is a challenge to work with. Nobody wants to integrate that curve. In truth, you can make some fairly simple approximations of the proportions of a cask, and the results you get from your calculations with that approximation will be pretty good. But we will have to keep in mind that the accuracy of our numbers is not especially high. Common methods for approximation are a 1) a simple cylinder, or 2) two truncated cones or conical frustums.
  • On the rare occasion that you do find a measurement for a particular barrel, the units are all over the place, which means that comparing apples to apples requires a spreadsheet. I have seen in2/gal, cm2/gal, cm2/L, and even gal/ft2!
  • The effective SA/V ratio in a barrel changes fast as the level of the liquid gets lower in the barrel. For example, by my calculations, by the time a bourbon barrel has lost 10% of its volume (often in the first year!), the contact SA/V ratio is 88% of that of a full barrel. I'm not sure what folks will do with this information except keep it in mind when they are aiming for a reasonable amount of wood in their spirits.
Okay. So what can we do to get good numbers? We can get a whole bunch of reasonably reliable numbers from industry, academia, hobbyists' approximations, etc., convert them to similar units, and see if the numbers tell a coherent story. Let's do that next. Red columns are gallons and inches, blue are liters and cm.
[tr][th]Name of Source[/th][th][color=#FF4000]Barrel Volume (gal)[/color][/th][th][color=#8040FF]Barrel Volume (L)[/color][/th][th][color=#FF4000]Interior Surface Area (in[super]2[/super])[/color][/th][th][color=#8040FF]Interior Surface Area (cm[super]2[/super])[/color][/th][th][color=#FF4000]SA/V (in[super]2[/super]/gal)[/color][/th][th][color=#8040FF]SA/V (cm[super]2[/super]/L)[/color][/th][th]Source URL[/th][/tr] [tr][td]Read Head Oak Barrels et. al[/td][td][color=#FF4000]52.8[/color][/td][td][color=#8040FF]200[/color][/td][td][color=#FF4000]6535[/color][/td][td][color=#8040FF]42161[/color][/td][td][bg=#FF8040][color=#BFFF40]124[/color][/bg][/td][td][bg=#FF8040][color=#BFFF40]211[/color][/bg][/td][td]https://redheadoakbarrels.com/barrel-info/barrel-dimensions/ https://www.deepsouthbarrels.com/page/barrel-dimensions/barrel-dimensions" onclick="window.open(this.href);return false;" rel="nofollow https://www.tallshipbarrels.com/blogs/barrel-dimensions/barrel-dimensions" onclick="window.open(this.href);return false;" rel="nofollow[/td][/tr] [tr][td]Schahinger and Rankine (1992)[/td] [td][/td] [td][/td] [td][/td] [td][/td] [td][color=#FF4000]53[/color][/td] [td][color=#8040FF]90[/color][/td] [td]https://www.extension.iastate.edu/wine/oak-aging-red-wine[/td][/tr] [tr][td]Brouweij Chugach (wine, nominal)[/td] [td][color=#FF4000]65[/color][/td] [td][color=#8040FF]246[/color][/td] [td][color=#FF4000]3401[/color][/td] [td][color=#8040FF]21942[/color][/td] [td][color=#FF4000]52[/color][/td] [td][color=#8040FF]89[/color][/td] [td]http://brouwerij-chugach.com/?page_id=940[/td][/tr] [tr][td]Pisoni Vineyards[/td] [td][color=#FF4000]60[/color][/td] [td][color=#8040FF]227[/color][/td] [td][color=#FF4000]3060[/color][/td] [td][color=#8040FF]19742[/color][/td] [td][color=#FF4000]51[/color][/td] [td][color=#8040FF]87[/color][/td] [td]https://pisoninotes.com/notes/barrel-sizes-matters-lucia-chardonnay/[/td][/tr] [tr][td]Wines and Vines Magazine article[/td] [td][color=#FF4000]59.4[/color][/td] [td][color=#8040FF]225[/color][/td] [td][color=#FF4000]3255[/color][/td] [td][color=#8040FF]21000[/color][/td] [td][color=#FF4000]55[/color][/td] [td][color=#8040FF]93[/color][/td] [td]https://www.winesandvines.com/features/article/166780/Barrel-Rescue[/td][/tr] [tr][td]Poppyseed Cellars[/td] [td][color=#FF4000]59[/color][/td] [td][color=#8040FF]223[/color][/td] [td][color=#FF4000]3178[/color][/td] [td][color=#8040FF]20503[/color][/td] [td][color=#FF4000]54[/color][/td] [td][color=#8040FF]92[/color][/td] [td]http://nielsj.users.sonic.net/3099/?p=48[/td][/tr] [tr][td]barrels and aging lecture slides[/td] [td][color=#FF4000]53[/color][/td] [td][color=#8040FF]201[/color][/td] [td][color=#FF4000]2824[/color][/td] [td][color=#8040FF]18219[/color][/td] [td][color=#FF4000]53[/color][/td] [td][color=#8040FF]91[/color][/td] [td]http://srjcstaff.santarosa.edu/~jhenderson/Barrels.pdf[/td][/tr] [tr][td]Brouwerij Chugach (whiskey, nominal)[/td] [td][color=#FF4000]53[/color][/td] [td][color=#8040FF]201[/color][/td] [td][color=#FF4000]2997[/color][/td] [td][color=#8040FF]19335[/color][/td] [td][color=#FF4000]57[/color][/td] [td][color=#8040FF]96[/color][/td] [td]http://brouwerij-chugach.com/?page_id=940[/td][/tr] [tr][td]OtisT’s calculation[/td] [td][color=#FF4000]49.5[/color][/td] [td][color=#8040FF]187[/color][/td] [td][color=#FF4000]2870[/color][/td] [td][color=#8040FF]18516[/color][/td] [td][color=#FF4000]58[/color][/td] [td][color=#8040FF]99[/color][/td] [td]via email, based on JD barrel measurements and reasonable assumptions[/td][/tr] [tr][td]Cylindrical 11”R 53gal “barrel”[/td] [td][color=#FF4000]53[/color][/td] [td][color=#8040FF]201[/color][/td] [td][color=#FF4000]2986[/color][/td] [td][color=#8040FF]19264[/color][/td] [td][color=#FF4000]56[/color][/td] [td][color=#8040FF]96[/color][/td] [td]my calculation. Radius- and volume-constrained cylinder[/td][/tr] [tr][td]Cylindrical 12”R 53gal “barrel”[/td] [td][color=#FF4000]53[/color][/td] [td][color=#8040FF]201[/color][/td] [td][color=#FF4000]2944[/color][/td] [td][color=#8040FF]18994[/color][/td] [td][color=#FF4000]56[/color][/td] [td][color=#8040FF]95[/color][/td] [td]my calculation. Radius- and volume-constrained cylinder[/td][/tr] [tr][td]Calculation using two truncated cones[/td] [td][color=#FF4000]53.2[/color][/td] [td][color=#8040FF]201[/color][/td] [td][color=#FF4000]3051[/color][/td] [td][color=#8040FF]19686[/color][/td] [td][color=#FF4000]57[/color][/td] [td][color=#8040FF]98[/color][/td] [td]my calculation - brute forcing volume with reasonable radii and length[/td][/tr]
I think the story is pretty clear. First, the "relative aging time" chart floating around on the websites of small barrel merchants is a load of bull. Second, the SA/V of 53 gal/200L American Standard Barrels is in the neighborhood of 56 in2/gal or 96 cm2/L. Those numbers are only about 5% lower for the larger barrels. If you are looking for measurements on slightly bigger or slightly smaller barrels than those in the chart you can probably interpolate the numbers safely.

I hope this post helps and can be a point of reference for future discussions about aging using oak. Cheers.

Re: Barrel Surface Area to Volume Ratio, Bourbon and Wine

Posted: Sat Nov 04, 2017 7:39 pm
by hpby98
Thanks for the informative post.

Looking forward to getting some aging in abit

Re: Barrel Surface Area to Volume Ratio, Bourbon and Wine

Posted: Sun Nov 05, 2017 5:54 am
by Single Malt Yinzer
Thanks for this post, it's really good. I added it to the wiki: http://homedistiller.org/wiki/index.php/Barrel" onclick="window.open(this.href);return false;" rel="nofollow

Re: Barrel Surface Area to Volume Ratio, Bourbon and Wine

Posted: Sun Nov 05, 2017 9:33 am
by OtisT
:-). Thanks for posting. I did some experiments recently using those red head numbers. Their chart looked really nice and also showed SA/V ratios for barrels from 200l down to 1l, which I found useful. F$@# me. Would be nice if we could scrub that chart from HD, so others don’t fall for their flawed numbers.

Thanks again for doing the math. :-)

Re: Barrel Surface Area to Volume Ratio, Bourbon and Wine

Posted: Sun Nov 05, 2017 10:42 am
by Badmotivator
My pleasure.

By the way, their numbers for surface area of the smaller barrels might be insane too. For example, to get a 20 L barrel with a surface area of 1382 in2, the barrel would have to be 3.6 inches diameter and 10 feet long. :)

Re: Barrel Surface Area to Volume Ratio, Bourbon and Wine

Posted: Mon Nov 06, 2017 11:02 am
by OtisT
Badmotivator wrote:My pleasure.

By the way, their numbers for surface area of the smaller barrels might be insane too. For example, to get a 20 L barrel with a surface area of 1382 in2, the barrel would have to be 3.6 inches diameter and 10 feet long. :)
No doubt. Don't trust any of the numbers on that red head chart. Lesson learned, do my own math as a sanity check.

And now I need to clean up one of my own thread where I used those numbers in one of my experiments. :x

Re: Barrel Surface Area to Volume Ratio, Bourbon and Wine

Posted: Thu Nov 09, 2017 9:52 am
by DeepSouth
I just took some measurements of my 15 gallon barrels from the Barrel Mill. They are about 24" long, 18" middle diameter, 15" end diameter, with 1" thick staves. The interior dimensions would be 22" long, 16" middle diameter, and 13" end diameter. Solving as two truncated cones with those dimensions, give a volume of 3644 cubic inches (or 15.8 gallons, so the math checks out), and an interior surface area of about 1680 square inches. The surface area to volume ratio for this 15 gallon barrel is therefore about 106-112 sq. in./gal. That's roughly twice as much as a standard 53 gallon barrel. From my experience with these, I'd say that's about right. 1.5 to 2 years is a good ballpark time range to age in a 15 gallon barrel in my experience, of course dependent on cuts, aging environmental conditions, etc. The various oak flavors that are extracted is only one component and needs to be in harmony with the flavor changes associated with evaporation, oxidation, and esterification

Re: Barrel Surface Area to Volume Ratio, Bourbon and Wine

Posted: Thu Nov 09, 2017 10:05 am
by DeepSouth
After looking a little more, they actually have the dimensions for their 5 gallon barrels on their website as 17" long, 12.5" diameter on ends, and 14" diameter in middle, with 1-1/8" thick staves. Doing the same excercise and solving for interior surface area as two truncated cones, gives a surface area of 894 square inches, and a volume of 1404 cubic inches(almost exactly 6 gallons, so I guess they are a little bigger in reality than their nominal 5 gallon size). For these 5 gallon barrels, that gives a surface area to volume ratio of about 149-179 sq. in./gal. That's roughly 3 times as much surface area as a standard 53 gallon barrel.

Re: Barrel Surface Area to Volume Ratio, Bourbon and Wine

Posted: Thu Nov 09, 2017 11:09 am
by DeepSouth
I have a hypothesis that when using small barrels, to approximate the aging time in a 53 gallon barrel, the formula should be something like this:

Small Barrel Volume=v
Large Barrel Volume=V
Small Barrel Time=t
Large Barrel Aging Time=T

And my proposed approximate aging time formula would be t=T/sqrt(V/v)

Say you are trying to approximate 4 years in a standard 53 gallon barrel. Using the above formula for a 1, 5, 10, 15, 30, and 53 gallon barrel using the above formula would give approximate aging times of:

1 gallon = 6.5 months
5 gallon = 1 year, 3 months
10 gallon = 1 year, 9 months
15 gallon = 2 years, 1.5 months
30 gallon = 3 years
53 gallons = 4 years

From anecdotal reports from other people aging in smaller barrels, these times feel about right.

Re: Barrel Surface Area to Volume Ratio, Bourbon and Wine

Posted: Mon Feb 05, 2018 12:01 pm
by Taxy
DeepSouth,

I am not a mathematician but I believe that, under the generally quoted hypothesis on barrel sizes and maturation time, that you would need to take the cube root from the V/v in your formula.

The generally quoted hypothesis is that the maturation time is proportional to the volume per surface area (v/a) when we have vessels with a identical shape and proportions but different sizes. In other words, twice as many liters per m2, means double the maturation time. I will work further on this hypothesis, although I am not entirely convinced.

In order to simplify the calculation, assume two cilinders C1 and C2 with an identical shape but different sizes, whereby their height h is equal to three times their radius: h = 3r. This is just an example to make the calculation easier but it will work for all two vessels (also cubes, balls and barrels) the dimensions of which have a fixed proportion, i.e. when they have the same shape but different sizes.

The hypothesis now translates as time1 : time2 = volume1/area1 : volume2/area2

Volume v of our cilinder:
v = πhr2 = 3πr3 (because we assumed h = 3r)
Surface area a of our cilinder:
a = 2πr2 + h(2πr) = 2πr2 + 6πr2 = 8πr2 [damn, writing math is html makes you go :crazy: ]

Now calculating volume v per surface area a
v/a = 3πr3 : 8πr2 = 3/8 r; so v/a is a function of r !

Now we can write our hypothesis as:
t1 : t2 = 3/8r1 : 3/8r2
or
t1 = t2 x r1/r2

So the maturation time is a linear functon of r1/r2.

r is a function of the cube root of the volume:
Volume v was v = 3πr3, so
r = 3rd root(v/3π)

In our case, this means
t1 = t2 * 3rd root(v1/3π) / 3rd root(v2/3π) ; or,
t1 = t2 * 3rd root(v1/v2)

This would mean that smaller barrels age less quickly than in your formula, i.e. 4y in a 53 gallon barrel would equal about 13 months in a 1 gallon barrel. This does somewhat go against anecdotal reports.

Re: Barrel Surface Area to Volume Ratio, Bourbon and Wine

Posted: Tue Dec 03, 2019 8:19 pm
by Badmotivator
The table I set up looks pretty well junked. Here's the gist of it as an image:
Screen Shot 2019-12-03 at 8.17.17 PM.png

Re: Barrel Surface Area to Volume Ratio, Bourbon and Wine

Posted: Wed Dec 04, 2019 11:47 am
by cayars
Surface area is just one of many factors.
The toast and char level of the barrel is very important as well.

Environmental factors such as temperature, barometric pressure, humidity play a giant role in angel's share.
The amount of seasons and differences in the swing temperatures from winter to summer play a big role as the spirit is pushed/pulled from the wood.
Keep in mind time on oak is only one component of aging. Store those barrels in Texas, vs Kentucky vs NJ vs Scotland and you will get drastic different results. Same as if you store them in your basement vs your attic vs your garage.

The spirits will go right on aging properly after being pulled from wood if put in SS barrels with proper head space and air changes. The tannin pulled from wood, the esters and other congeners will continue to transform over time regardless if wood is present or not. It will surely develop differently but will continue to develop.

What I think these surface area calculations help most with is to make sure you don't over oak to quickly but don't really truly cover aging (just part of it).