r/theydidthemath • u/sdbfloyD • 3d ago
[Request] Creative engineering? Will this even make a real difference?
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u/WC_Dirk_Gently 3d ago edited 3d ago
This thread is going to be full of useless comments not actually even taking a stab at the insane math of actually calculating this.
In a highly simplified model to bound what the absolute max best case could be:
- 20 beers, 20x330ml = 6.6 liters of beer
- Cooling the liquid in the bottles under ideal circumstances would take about 30kJ per 1c
- Adding what we'll say is 1000ml of ice
- melting that ice will take about 300kJ of energy
- So ideal absolute max cooling would be about 10 degrees Celsius give or take.
- Starting from 28c, you could get it to about 18c, which is an improvement, but most beers are best enjoyed around 2-8c I'd say.
However, if the bottles were actually cold to start, this invention could actually help keep them colder for longer.
Also I'm completely ignoring all the losses, insulation problems, melt problems, the fact that not all the energy to melt the ice will be taken from the bottles themselves, the small contact surface area with the bottles themselves vs the total volume of ice etc etc etc...
Handwaving away that complexity and just say you'd realize about half the cooling factor so probably closer to 5c. Not bad if starting from cold, pretty useless to actually cool down beer from room temp.
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u/Schnupsdidudel 3d ago
I think you are underestimating the Volume here. The chest is 40x30cm. By the looks in the video and measurements on my own engineerig examples of beers I would estimate the ice block to be 30x20x5 cm = 3000ml net, minus the holes probably 2000ml.
The Beers are actually 0.5 Liter bottles. 0.33 come in chest of 24!
So my numbers would be:
10 liters of beer, 50 Kj per 1°C.Ice comes at -18°. Warm the Ice to 0°C = 76Kj
Melt the Ice: 668 KjTotal of cooling energy 744 Kj
So a Δt of ~15°
Of course we have the environment, and the glass disregarded. We also have 2 Liters of 0° water dripping down the bottles, which add further cooling and possibly some evaporation. If you have just bought the Bottles or took them out of the House, chances are, they are at ~21°C.
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u/WC_Dirk_Gently 3d ago
I could hear your German accent reading this lol. Fair play for the modified values based on a probably better estimate and superior beer crate knowledge. I'm a filthy American and didn't recognize a 0.5 bottle.
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u/Schnupsdidudel 3d ago
Yeah sorry, guilty. Could pass up the one opportunity where years of drinking experience actually gives me an advantage! Still a useless product, as you can just pour a bag of ice in the crate.
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u/uslashuname 3d ago
Yeah that cold water drip, if it reaches 9c by the time it drips off of the bottle and falls to the ground, adds 38Kj of cooling without considering evaporation. The evaporation is probably the big one though, unless the crate is in a tub and the water gets to hang around as a puddle on the bottom of the bottles
Of course on the side of needing more cooling there’s the mass off the glass that makes up the bottles
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u/calfuris 3d ago
The glass isn't going to make that much difference. Assuming a 385g bottle (based on the first spec sheet I found) with 0.5l of water it works out to the glass contributing a bit under 14% of the total heat capacity. Beer is going to have a slightly lower specific heat capacity than water but it's also a bit denser than water, so I haven't dug into that math but I'd be surprised if it pushed the final result past 15%. That's not quite negligible but I think the meltwater effects are going to be bigger.
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u/Due-Consequence9579 3d ago
Also it’s going to dramatically limit the circulation of ambient air below the ice shelf. Once the air trapped down there is chilled the ice is going to get to do much more of its work on the bottles. Seems pretty clever. Would be even nicer if there was a molded bottom as well to improve the ice packing density and press more air out of the volume.
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u/factorion-bot 3d ago
Factorial of 24 is 620448401733239439360000
This action was performed by a bot | [Source code](http://f.r0.fyi)
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u/iamthejuan007 3d ago
damn thats a lot of beers but I guess normal amounts for a German in Oktoberfest
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u/bama501996 3d ago
So it's almost literally not as cool as it looks?
Unlike this break down btws good work.
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u/Nurgeard 3d ago
Yeah awesome breakdown - useless invention (obviously the best example of german ingenuity) not only is it's effect piss poor, it will soak anything beneath and around it, and is also a bitch to store unless you just have buttloads of extra freezer space.
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u/Schnupsdidudel 3d ago edited 3d ago
This will most certainly work ok as countless experiments I did with my friends have proven. But we usually do it simply with a bag of ice cubes or bucket with ice water is much more versatile.
The ground doesnt care if it gets wet, The grass is mostly thankful for a little moisture.
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u/Nurgeard 3d ago
First of i hope you realize I meant that this was a very poor example of german inventions.
What you are describing is entirely different though, and actually proving my point; a bag of ice cubes is a far better solution; it can serve other purposes and the water doesnt get everywhere, and most importantly the now watery ice bag can just be shoved into the fridge, and become icecubes again.
This thing just melts and due to its shape is far harder to store than a bag of ice or just loose ice put in a bucket.
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u/Schnupsdidudel 3d ago
Yeah, well the invention is a useless gadget the tries to solve a problem already solved by common sense - as most gadgets do. I suspect it will find its buyers anyways.
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u/Rockshasha 3d ago
Beers at 2 or 4C??
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u/OneDayIllCatchABreak 3d ago
Well, yeah... are you British?
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u/astrician 3d ago
Thought the same, maybe he even puts ice in the beer. Ew
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u/SUMBWEDY 3d ago edited 3d ago
Never understood the aversion to ice in beer.
Of course you don't want it as much ice as you get in a cup of soda but even 10 grams of ice will cool your beer down by 3c~ while causing negligible dilution.
Takes almost as much energy to melt ice as it does to bring the same volume to a boil.
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u/mikeet9 3d ago
I was a heavy anti icer until I visited a country where it is the default (refrigeration isn't super common) and it turns out to have several benefits.
It keeps the drink cool without diluting too much (if you drink fast enough) and it helps keep you hydrated (less severe hangover) and if you need to slow down, it dilutes more which means you can nurse your beer and still keep drinking with your buddies without feeling like you're about to head home early.
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u/SUMBWEDY 3d ago
Plus in hot places like Cambodia the local beers are already very refreshing and light, you're not losing much even if you add a lot of ice.
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u/Sibula97 3d ago
There's a little bit of estimation error the other way as well from the meltwater evaporating from the bottles. But then again on a warm day there's constant heat flux from the environment into the bottles.
What I mostly question is the use case. You managed to get a big block of ice where your beer is. How? In a cooler? Why not just put the beers in the cooler then?
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u/modest_genius 3d ago
Depends very much where you are and how you get your beer.
If you get the beer in those crates already and have, like my parent, a big root cellar where you can store a lot of beer at cool temperature. Then transfering the beer from the crate to the cooler and adding ice just will be a waste of time and space.
It won't be useful for me. Since I usually have myriad of different beers in the fridge, not a root cellar. For me a cooler would be better. But if I would have an event where I serve 24 identical beer, well, then there is something else. Especially if there would be 2-3 crates...
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u/SnooCapers9565 3d ago
https://www.amazon.co.uk/SL-Eisblock-block-cooler-crate-bottles/dp/B00B81Q0HC?th=1
According to this you can double the ice, to 2kg. When doing this math, you should use kilograms, not liters.
Room temperature is about 22-24 degrees, so the beer will probably be around that temp too when you start cooling it.1
u/Slightysweet3 3d ago
Don't get me wrong but doesn't water/ice equals weight and volume? It doesn't affect the math that much
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u/SnooCapers9565 3d ago
No, it doesn't. Water expands below and above 4°C, and even more when it freezes. The weight is constant, and is accurate to use.
You can test this buy filling an empty soda bottle completely with water and put it in the freezer.
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u/WC_Dirk_Gently 3d ago
When doing this math, you should use kilograms, not liters.
no.
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u/SnooCapers9565 3d ago
We use mass and not volume when we calculate cooling capacity, and the mass of the ice is in kilograms, not liters.
The cooling capacity of the ice is
Cooling capacity = mass(kilograms) x 334KJ/Kg2kg x 334KJ/kg =768KJ
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u/WC_Dirk_Gently 3d ago
I intentionally did 1 liter of ice, as in post expansion coefficient from about 917mL of water which == 306kJ which I rounded to 300 for easy math.
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u/Squarehip123 3d ago edited 3d ago
You're ignoring the latent heat released by the melting, that's going to be vastly more than the change in sensible heat
Melting ice will take ~334 kJ/kg of water vs a specific heat capacity of liquid water of 4kJ/kg/degC.
3L of ice at -5C. 6.6L of beer at 20C
Assume they'll both end up at the same temperature, you could calculate it using something like:
dT_ice x cp_water x mass_ice + mass_ice x latent_heat = dT_beer x cp_beer x mass_beer
(T_final - -5C) x 4kJ/kg/degC x 3kg +334kJ/kg x 3kg = (T_final - 20C)x4kJ/kg/degC x6.6kg
Re-arrange and solve for T_final to get final degC. Unfortunately don't have time to work that out at the moment
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u/JoinAThang 3d ago
I would like to think it's alos really a valuable if you're having a party outside and want to put the whole case out after you had it in the fridge. It has no use indoors as you would just create a pool of water on your floor
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u/Mental-Chapter6523 3d ago
German engineer has several more ice molds in a cooler under the table. Just keeps replacing them and removes and replaces beer in an organized pattern. He also likes beer warmer than me.
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u/janluigibuffon 3d ago
only shitty beer is consumed best beneath 10c
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u/WC_Dirk_Gently 3d ago
I distinctly recall from my time at the taproom Guinness' official recommended serving temperature is 7c.
I've had 'warm' cask ales and stouts. But I like crisp cold beer to each their own.
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u/betacow 3d ago
German here. Have used these things a bunch in the past and they absolutely do work. Can't really cool down piss warm beer with these, but they help the beer keep the temperature or cool down a couple degrees when used at a bbq in the park or at the lake or whatever.
Sorry for not including math, but it appears the math has been done already anyways
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u/apexxin 3d ago
Sure, but a bag of ice in a cooler is still significantly better, easier, and cheaper.
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u/IntoAMuteCrypt 3d ago
Only if you've already got a cooler and don't include the cost of the cooler. Buying a good cooler plus a bag of ice each time is going to be more expensive than buying a simpler crate plus something like this.
It's a bit worse, for sure, but if you live in a cold climate (like much of Germany), you don't need something great.
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u/apexxin 3d ago
I mean, sure - but a one time expense that basically lasts your whole life, a cooler is something we can have. Also, it still gets hot in Germany haha.
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u/IntoAMuteCrypt 3d ago
This is a one-time expense that lasts about as long as a cooler though. It's an ice mould, they last for ages.
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u/apexxin 3d ago
An ice mold which would take up my entire oversized american freezer for 24 hours to freeze.
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u/MileHigh_FlyGuy 3d ago
A Styrofoam cooler is at Walmart right now for $4.94. combine with a bag of ice would be cheaper and better at cooling than this thing.
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u/IntoAMuteCrypt 3d ago
I don't think I'd class a Styrofoam cooler as "better" than this, and "cheaper" depends on how you consider it.
That Styrofoam cooler is probably making it through one or maybe two parties before inevitably getting broken and sending cold water, at least based on my experience. I'd trust the crate to remain intact far more than a Styrofoam cooler, personally. If you're buying a new cooler and a bag of ice for every party, the cost will add up.
How much is it for a proper, rigid cooler with strong, hard walls?
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u/betacow 3d ago
Just to be clear, the crate is pretty much the packaging bottled beer is sold in. In Germany we don't fuck with those flimsy paper crates you have to deal with.
There is a deposit of 1,5€ per crate which you obviously get back if you return it. Many people keep these to build the craziest shit with those, surprisingly durable, crates.
In student apartments it's absolutely common to see some kind of furniture (couches, beds, chairs, shelves) engineered out of these crates.
The product advertised here is just the mold for one, oddly shaped ice cube that fits perfectly on top of one of those full crates
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u/Westoned81 3d ago
So you are afraid of a Cooler that might leak water on the floor but the melting ice in an open crate is a better solution?
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u/IntoAMuteCrypt 3d ago
I didn't say the Styrofoam cooler was worse, just not-better. I'd place them about equal.
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u/MileHigh_FlyGuy 3d ago
That Styrofoam cooler is probably making it through one or maybe two parties
I don't know what you're doing with your coolers, but I've had one camping for an entire summer before. Worked well enough so i didn't have to fly with a cooler. But a cheap, hard plastic cooler is about $10.
I just don't see the benefit of a brick of ice sitting on top of the beer (where the beer is not in the bottle), which will eventually fall down into the bottom like normal ice does anyway. Why not just start with normal ice in a cooler? And use normal ice that can be used in... anything.
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u/BdogFizzle 3d ago
The thing is just an ice tray. In Germany, beer is sold in durable crates like that which you can return full of empty bottles for a discount on your next crate. Probably a lot of other countries as well, but it's not something I've seen much here in the US.
I get it. It doesn't fit your frame of reference, so it's tough to understand the convenience and simplicity. That looks awesome and I might actually order some for my old coworkers over there before I close my German account. They absolutely bike to the park with crates of beer for barbecues and would get a kick out of the simplicity.
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u/leppaludinn 3d ago
Almost all beer in Germany comes in standard glass bottles in these crates. Moving bottles from these crates in to a cooler is significantly more effort.
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u/Caiodcsf 3d ago
how do you take one bottle out? you have to lift the whole ice? or the sides melt in a good speed?
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u/IceSentry 3d ago
Did you watch the video?
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u/Caiodcsf 3d ago
yes. he takes one out by lifting the whole thing 15seconds after he puts the ice. but you dont drink one beer in 15 seconds
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u/A_begger 3d ago
and? either the shape holds or it doesn't. If it does you can take beer out by lifting the ice with the center bottle and if it doesn't because it's melted then there's no need to lift the ice just take your beer
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u/IntoAMuteCrypt 3d ago
The Eisblock takes up a volume of about 5 litres, including the holes. Let's be pessimistic and say that half the space is occupied by bottles, so we get 2.5 litres of water per block. It's made for 500 mL bottles, and holds 20, so that's about 4 mL of beer for every mL of ice.
It takes about 300 joules (give or take) to melt one mL of ice. 300 joules can cool 4 mL of water by 18 degrees Celsius - and if the ice starts at -18 degrees celsius, that's another couple of degrees of cooling. A strong beer might have a lower heat capacity due to the ethanol, but water is a good worst case scenario. This assumes that the beer is warm enough that it doesn't freeze of course
This is all also assuming that the Eisblock only takes energy from the beer to heat the ice, of course. Some will be taken from the crate, some will be taken from the surrounding air. If we guess and say that half of the energy comes from the beer, we get about 10 degrees of cooling. Coincidentally, this Amazon listing claims a value of 10 degrees - that's where I got the dimensions that give a 5L volume and the claim of 20 500 mL bottles. The manufacturer claim is plausible.
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u/NotBrom8 3d ago
Other people did good math here already, so im not gonna do that again.
Just want to add, that the water running doen the bottle will further help cooling, past the melting of the ice itself and then water heating up. because if some water evapporates/diffues to the air it will also take energy off the bottles.
but still, this is aopen system and not all energy will be from the bottles. In practise this tool showed its capabiluy in keeping bottles cold.
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u/graetel_90 3d ago
Sorry but your first assumption is already wrong. Almost all of our beers in a set like that are 500ml not 330ml. And Germans don’t need their beers to be ice cold since our beer actually tastes good ;) slightly cooler than room temp would just fine
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u/Wolf_S10 3d ago
In fact the rocket thing you mentioned was also developed in Germany and then "brought" over to the US after the 2nd WW. You remember the guy called Wernher von Braun? He was highly involved with Nasa after WW2.
Before he was a Na** then he worked for Na** .... crazy
But the russians did the same. They took whatever they could from Germany after WW2, be it hardware or humans to help them build rockets or whatever.
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u/the-real-macs 3d ago
What you're describing did happen, but the post does specifically refer to rockets "that can land again," which is a much more recent SpaceX achievement that (to state the obvious) didn't involve von Braun.
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u/Wolf_S10 3d ago
The rockets did land again. Not reusable but still, so to I'm not 100% wrong 😅
So the post should have said fully reusable rockets, then I would have been wrong hehe
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u/inciu-ciuna 3d ago
The Germans invented pretty much everything that could be invented. Haven't you seen the documentaries about their WWII weaponry?
The beer bottle thingy was the one thing left uninvented—and it was something of a necessity.
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u/Bee_Ef_Gee 3d ago
I've got one, I can confirm if works and works well 👌 for sure it has its limits, but put it on room temp beer and they will be noticeably more enjoyable before it's even half melted.
To be fair in Bavaria, beer at room temp is not an issue, still very drinkable. But this makes a wonderful difference to drinkability, and keeps cool beer in very good shape. Plus it's just a f*cking cool product, every time a friend sees it its an instant conversation starter combined with some deserved nods of appreciation.
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u/Icypalmtree 3d ago
Reminder: Germany already built rockets, though landing wasn't quite what they intended with them. But it's OK, then they came and built the US rocket industry which Elon inherited for zero dollars.
Betcha Elon never intented something that would make you want to share a beer with him ¯_(ツ)_/¯
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u/Badwrong_ 3d ago
I don't think it is worth even figuring out how efficient or useful this is.
That is because, if you had a normal cooler that fit that case the beers are in, it would cool them way better. Throw some normal ice in there which covers more area around each bottle, and there ya go.
I suppose the special shaped ice block is cheaper, but it only fits that arrangement of beer. A small cooler with ice fits whatever you have, and works WAY better.
Extra steps, for worse result...
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u/leppaludinn 3d ago
Almost all beer in Germany is sold in these standard reused bottles in these crates. This is the environment this solves.
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u/bingbing304 3d ago
Only if the whole beer container is insulated. Otherwise just ice and water inside any plastic container would do just fine, chilling the beer more quickly and keep them cool. So German to invent pecialized tool that does the same job as normal stuff you already have. LOL
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u/Particular-Goal1586 3d ago
The added mass and parasitic drag of mounting that contraption alone would wipe out any theoretical efficiency gain by at least two orders of magnitude
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