Optimum ratio of pot diameter to height

[Redacted k]

I have seen various discussions regarding the optimum ratio of pot diameter to pot height for a given volume. Wanting to answer this for myself, I built up a spreadsheet to tabulate numbers on this.

I made the assumption that all pots are made of the same thickness and material. Handles and any rounded or rolled edges are neglected. The optimum size is not affected by the thickness or material chosen.

The results are:
Neglecting the weight of a lid, the least weight for a volume occurs when the diameter of the pot is twice its height. For a 500ml pot, this occurs at about 4.25" diameter and 2.125" height (forgive the mixed units, they are for my convenience not yours)

Assuming a lid of the same material, the least weight occurs when the diameter is the same as the height. For a 500ml pot, this occurs at about 3.4" diameter and height

The takeaway: If you are going to use a pot with a lid made of much lighter material, such as foil, then you want the diameter to be nearly twice the height. If you are going to be using a pot with a lid of the same material and thickness, or one of the frying pan lids, you want the diameter to be about the same as the height. Choosing the option with a "thick" lid will weight about 1.25 times that of no lid.

Happy to share the spreadsheet, just not sure how to nicely post it in the thread. Far too many numbers to present cleanly.

Given the trends noticed for heating efficiency of a stove increasing with greater pot diameter, I think this suggests that we should use wide, short pots with foil or carbon lids.

[Jerry Adams]

what kind of stove?

did you measure weight of fuel used, temperature difference of water?

[Daniel Pittman]

Never mind Jerry's post. I actually read your post and comprehended it. Good work! What I need now is for someone to test boil times to compare efficiency between thick lids and foil lids. The Stock lid for my ti kettle is pretty sweet, but if foil works just as well I might ditch the lid.

[Daryl and Daryl]

Patrick,

Nice piece of logic leading to a useful conclusion.

Sherlock Holmes would approve.

[James Marco]

Yeah, I follow. I do not think it is quite as simple as that, though.

1) Stove output would effect pot diameter for best heating. I have mane a lot of alcohol stoves from ones with small diameter holes, to large "flame thowers". Small diamer pots do not work as well with larger stoves. 10" diameter pots (aka fry pans) don't seem to improve the efficiency of small diameter stoves. You carry weight to no measurable effect.
2) Depending on the wind screen/heat screen you carry, it may help with boil times to go with a "square" stove. For example, a caldera cone for a fosters can will likly not achieve a boil as fast as a grease pot/caldera cone, given the same volume of water to be boiled (about 17oz or ~500ml.) But, the fosters/caldera set up is lighter.

Even using canister or WG stoves, if turned down low (rather high efficiency burns) you might find a them to be useless with too wide pots. But your numbers do show a good approximation.

[Marko Botsaris]

Yeah, the fuel efficiency, or in some case like the cat stove whether it can even bring off a boil of 2 cups at all, depend on the ratio as well.

This is why we will never get bored discussing stoves and pots on here. :-)

James, if you can just give us a simple formula for the fuel efficiency as a function of the geometry we can generalize the optimization. So it should be simple – right?

[Delmar O’Donnell]

Interesting. So…optimum ratio for WEIGHT. I wonder if there is also an optimum ratio for heat transfer/speed of boil (for a given stove), and a best-possible-compromise of the two variables.

I've long suspected that squareish-profile mugs (think Imusa mug or MSR Titan mug) found that sweet spot, but never had anything but intuition to go on.

Wide short pots–ie, pans–are great for sucking up heat, but do present some design challenges, particularly in designing windscreens for them.

[zorobabel frankenstein]

You also have to take into consideration the risk of spillage of the heated/cooked content. I usually leave at least 1.5cm of the pot height unfilled as a safety net for boiling, handling or cooking on a surface not perfectly horizontal. The risk of spillage from the last 2 spillage factors is worse for wide pots compared to square ones.
When you take that lost volume into consideration, I'm not so sure the wide pots are the best for the weight.
Other things to consider: foil lids work better for narrower pots; wide pots don't work well with wire bails.
Can you tell I prefer square pots?
When melting snow, I use a wide pot though (with a Whisperlite), as a square pot would be too big in a diameter suitable to the Whisperlite.

[David Thomas]

If you got a height = radius (height = 1/2 the diameter) for the no-lid scenario, you got the math right.

But then there's that assumption of constant wall thickness.

Could you have a gallon paint can with soda-can thickness?

Do you need paint-can thickness in a soda-can diameter?

Nope and nope.

For burst strength, wall-thickness must increase linearly with diameter. And there is something similar going on in crush strength (does the pot get easily bent out of round in normal handling and packing). Those factors require you scale up wall thickness in larger diameters and with higher heights.

And then there's denting and wearing through. Rubbing a soda can across a rough metal stove support and you'll wear a hole in it. Those put a lower limit on wall thickness in small diameters.

Everyone keeps asking, what about stove efficiency? A somewhat wider pot will capture more heat from the flame than an excessively narrow one.

As Zoroblaster (sp?) points out, you want some "free board" so avoid sloshing your contents out of the pot.

I jiggle all these factors around in my head and add some engineering judgement and I end with something close to Jetboil's pots – HX fins to capture heat in a small diameter while allowing a thin wall and enough height for minimal sloshing.

If constructibility was no issue, and you only wanted to heat up water, you'd end with a miniature water heater. Flame exhaust going up the middle of a tall vessel with HX fins (or at least turbulence generators) in that tube and lots of insulation around the outside of the vessel. No moving parts and you get 82-85% heat recovery versus 30% in a simple pot and 50-ish% in a HX pot. "But the chimney would be too small for my canister stove!" True that, but if you were capturing 2.5x more heat from an esbit tablet. . . .

[Marko Botsaris]

Yes, there should be an optimal ratio for heating efficiency as well, for a given stove with the height above the stove an additional parameter. Unfortunately it should depend pretty sensitively on the stove type and geometry, jet orientations, and so on, and since it involves fluid mechanics (for the way the hot air streams past the pot) as well as heat transfer it probably isn't simple – especially the fluid mechanics part. You would probably need to do computer simulations – short of having a set of pots for all the different geometries so you could do it experimentally.

Possibly we can lure one of the experts away from their work on global warming and get them to work on something really important for a change. ;-)

[Delmar O’Donnell]

You just never know how interesting a conversation is going to get…! Good stuff, guys. I'm feeling smarter already.

[Marko Botsaris]

There is a story that famously nerdy and clueless Physicist Paul Dirac at a cocktail party argued that there was an "ideal distance to view a woman's face" since if very far away you couldn't see it at all, and very close all you could see was a small patch of skin. That is all we are doing here with the stove and pot (minus the sexism).

Needless to say with conversational banter like than Dirac was not known to have often been offered the chance to view a woman's face from the ideal distance.

[Dan @ Durston Gear]

Lots of good points here.

A few more considerations:
– Larger diameter pots require larger diameter windscreens, which is more weight.
– If you want to pack a cone inside, either tall or wide works better than equal dimensions.
– Very tall slim pots make it tough to stir the contents
– Wider pots are more stable.

My guess is that pot weight doesn't vary that much for a given volume & material unless you're into extremely wide or tall shapes. Overall I tend to like pots about equal dimentions (diameter = height) or slightly taller.

[Redacted k]

Regarding windscreens,
I have noticed the same thing I have seen mentioned here a few times. Having a windscreen wrapped all the way around the pot, for Most of the pot height, yields outstanding heat exchange. I get some unreal boil times using about a 1/4 inch space between pot and screen, using my open country 4 qt and gravity mf stove.

I suspect all of these other weight factors can be factored in, things like windscreen, head space between liquid and top of pot, and lid thickness.

Regarding variable metal thickness, you are academically correct. In practice, it is reasonable to say that all equivalent quality and materials will be about the same thickness, for a given capacity. Yes I know snowpeak uses thinner ti than toaks, don't get lost in the minutia.
If beverage can durability works for you, only look at and compare beverage cans. The same applies if you will only consider stainless that can bounce off a rock without damage.

Regarding the most efficient being a water heater, I believe the camping version of that is called a Kelly kettle. For the just add water to bag crowd, it may be an alternative to the jetboil type pots.

Definite trends from these numbers, you are rarely well served by a pot that falls outside of the 1-2 range of diameter/height. Within that range, weight differences are pretty small, but that is the margin this community obsesses about.

[Charley White]

To distill what many seem to be saying and I naively think to be true: the optimum shape–minimum weight–for a light containment vessel is that with the least surface area per liquid volume. That is the ratio stated. OTOH, the optimum shape for heating contents is almost the opposite–maximum (heated) surface-to-volume ratio. Into this is mixed all utility considerations for best design.

I have a question, though. I note a common acceptance here that heating happens best below. Is this well understood? Again naively, I can conceive how more heat is "directed" at the water when heat is below it, and more is directed "up and away" in hot gas rising up the sides–even with laminar flow disruptors. But I also remember a youtube of an alcohol stove with flames rising ONLY up the sides, and the assertion this was as efficient. Hooey?

Per DThomas, I am a little surprised you don't see more center-chimney boiling pots. Pretty unwieldy design in many ways, but still… Got some sterno heated soup in a Thai restaurant in such a vessel once.

[Eric Blumensaadt]

It's been pretty well determined in the past that for most stoves pots that are wider than their height works best.

And the 2:1 ratio of width v.s. height looks good.

My 3 cup anodized aluminum pot that came with my CC Sidewinder stove is about that ratio, as are all my other larger pots.

Caldera Cones (IMHO) seem to maximize that 2:1 ratio with ther ability to contain heat around the sides and prevent heat loss from windy conditions. Not so most other stoves, even those with heavy foil wind screens – I know from experience.

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