Optimizing Canteen Cups

Yesterday I happened across this webpage.
This is a concept that I have encountered before: that the optimum proportions for a cylinder are to have it at a height equal to its diameter.
The non-calculus explanation for this goes something like “a sphere has the lowest ratio of surface area to volume and a cylinder of equal diameter and height is closest that a cylinder can get to a sphere”.
Optimum use of materials means less weight to carry. 
You would think there would be a special name for such a cylinder so proportioned, but if there is I have yet to encounter it. Update: Equilateral Cylinder.
This concept can be applied to the design of hiking and survival gear.
Yesterday I wrote a little about canteen cups and muckets. In a previous post I mentioned a idea that a good size for an eating vessel was around half a litre.
If you have to travel light, your main, probably only, cooking vessel will be a canteen cup, and this will also serve as your bowl and your mug.
Most of us have to make do with whatever we can get, which is usually a military design.
Perhaps our most important, most likely cooking vessel deserves greater consideration?
Let us imagine we are designing a better canteen cup. The above concepts may play a part.
The typical military canteen cup has a kidney-shaped cross-section. They are designed with the assumption that they will be carried with a water-bottle, and that that bottle may be worn on the belt.
Assumptions are always dangerous beasties, and should occasionally be tested to discover if they have gone rogue!
(Military water bottles of kidney or oval section date to at least the 18th century and therefore predate their being worn in belt pouches!)
Obviously, carrying a supply of water on your person is prudent. Depending on situation and other factors this may be anywhere between 500 mls to 2 litres. Larger volumes should be considered a pack item.
Your typical military water-bottle is not the best way to carry water on your belt. If you land on it when falling or taking cover, it can hurt or bruise you.
If it is only partially filled, noises of water sloshing may betray you.
Many designs have a cup that fits over the top of the bottle, meaning you have to remove this and keep it safe every time you want to drink from the bottle. That snap-link I told you to attach to your webbing can prove useful here, but this can still be a hassle when you are half-way up a windy hillside and trying not to drop your rifle or lose sight of your mates.
For the above reasons a lot of soldiers and outdoorsmen now prefer bladders with drinking tubes such as Camelback and Platypus.
Does the cup need to fit outside a water-bottle? That interior space can be put to use for lots of other useful items. A hank of cord, fuel tablets and/or tube of alcohol fuel paste, small medical kit, sewing kit, spare lighter, tea and coffee bags, instant soup, OXO cubes and so on.
Does the cup need to be on your belt?
Generations of British soldiers will probably disagree with me here, but usually a hot cuppa is not life and death.
Your survival gear should be at skin level and your belt/webbing reserved for immediate use items: ammo, a good knife, a couple of litres of water, CI-IFAK trauma kit.
Your canteen cup should be a pack item, preferably in a readily accessible side-pocket.
What is the ideal shape for a canteen cup?
A spherical vessel is not really practical for a number of reasons. A hemispherical bowl of around 500 mls capacity will be about 12 cm/5" across and 6 cm/2.5" deep. Such a bowl can be used for both eating and drinking from but may not be the best shape for a cooking vessel. Woks generally need to be wider.
A cube of around 500 mls capacity has 8 cm sides. The corners of a cube may be difficult to get clean with a vessel of this width.
Another space-efficient option is a half-cube, 10 cm square and 5 cm deep. This has potential. This might resemble a smaller, square-section version of the familiar British Army mess-tin. Plenty of tea has been drunk from these, but it is not the best shape for a mug.
This brings us back to a cylinder of equal diameter to height, or thereabouts. For a capacity of about 500 ml, height and diameter will need to be around 9 cm/3.5".
This seems wide enough to eat out of and keep clean, deep enough for cooking and drinking. On the other hand, this shape may be too wide for easy carriage in a back-pack side-pocket.
This suggests that our canteen cup should be flattened in cross-section, and if we take this route we might as well give it a kidney-shaped cross-section. Realistically, most end-users will probably not buy a canteen cup unless it is this shape!
There is probably an optimum ratio of height to end-size for a kidney-section vessel, but the calculus is beyond me.
The above figures are based on another assumption: that we want a volume of around 500 mls.
Looking at four of the metal canteen cups I own, there is a notable difference in sizes.
The British Crusader Mk1 is noticeably bigger than the US (actually Dutch) cup and the upper cup from the Bundeswehr M59 canteen. This may partially be so the Crusader can fit over the bottom of the Osprey waterbottle. The Osprey has a plastic mug that fits over the top (!).
Theoretically you can carry both this mug and the metal Crusader around the same bottle. In practice you are better leaving the plastic mug for kit inspections. Also notable is that the Crusader Mk2 has a larger capacity than the Mk1.
A quick exercise with a measuring jug and some water yielded the following approximate volumes:
  • German M59 upper cup: 450 ml
  • Dutch canteen cup: 500 ml
  • Crusader Mk1: 650 ml
  • Crusader Mk2: 800 ml
The Dutch cup appears closest to our theoretical ideal. This is about 13 x 8 cm across and 9.5 cm deep. I don’t know if that is optimal, but the basic shape has not changed since 1910!
The Dutch cup is a sound choice for your emergency kit, but the British cups are ahead on features such as non-stick coatings, measuring marks and accessories. 

Even more interesting was weighing the cups. The Dutch cup was 9.4 oz/266 gm, the Crusader Mk 1 was 9.7 oz/275 gm yet the larger volume Mk 2 only 6.9 oz/195 gm.
What this boils down to (pun intended) is that most of the commonly available choices are fairly sound, but there is room for improvement.
While issues such as lids and bail handles need addressing, optimizing proportions could save additional weight.
A smaller version of the Crusader Mk2 would be an attractive product.