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, but if there is I have yet to encounter it.

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!

Obviously, carrying a supply of water on your person is prudent. Depending on situation and other factors this may be anywhere between 500mls 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 items: ammo, a good knife, a couple of litres of water, 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 500mls 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 500mls capacity has 8 cm sides. The corners 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 to a cylinder of equal diameter to height, or thereabouts. For a capacity of about 500ml, 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 500mls. 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 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: 450ml
• Dutch canteen cup: 500ml
• Crusader Mk1: 650ml
• Crusader Mk2: 800ml

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 9.4oz/ 266gm, the Crusader Mk 1 was 9.7oz/ 275gm 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.

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What's a Mucket?

Today I was woken from my slumbers by a hailstorm rattling against my window. When I was a young boy I was very interested in spiders and read many books about them. Even with this knowledge, it still impresses me that a flimsy looking cobweb caught so many hailstones, so they appeared frozen in mid air.

My day started with me being reminded of old knowledge, so I was pleased to discover something new while I drank my coffee:

I came across the word “mucket”. Most sources will assure you that a mucket is a variety of bivalve, resembling a mussel. But it was also used for a much different beast. 

Mucket is presumably a portmanteau of “mug” and “bucket”. Alternate names are “coffee boiler” or “boiler cup”. The sites offering them for sale are mainly geared to supplying American Civil War reenactors. Some of the examples offered us the original construction methods and materials such as soldered tin, which is less than ideal for actual use. Others look the part but use modern construction and materials such as stainless steel.

I have been planning to write a post on canteen cups, but I am holding off until I can get around trying to make lids for mine. At around 24 fl.oz (c.710ml) the mucket fills a similar niche to the modern canteen cup, but I have to say it is ahead on some of its features. The mucket has a bail handle so that you can hang it over a fire. And not only does it have a lid, but one that is attached by a hinge, at least in some examples I have seen! The lids have a ring, allowing you to raise them with a stick or similar implement rather than burning your fingers. Admittedly, it is not kidney shape in section, but since a canteen cup (or mucket) should be in a pack rather than extra weight on your belt, this is a minor issue. Camouflage not being an issue, the Civil War soldier hung his mucket outside his ration bag.

Hopefully some manufactures will have a good look at the mucket and design more capable canteen cups.

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Umbrella Fighting in PDF

My series of articles on self-defence with an umbrella, cane or similar objects have now been combined into a single document. 

Umbrella Fighting

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Sun-Compass

Yesterday’s topic logically brings me onto today’s, and another ancient but useful navigation device.

If you have even just glanced through a survival manual you will most likely have seen the shadow-stick method. I have previously described this in the context of navigating by the moon. The moon and stars also rise in the east and set in the west. The more usual context for the shadow-stick is using the sun.

 

The method is simple. Place a stick or similar in the ground so that it casts a shadow. Mark the end of the shadow. Wait for at least twenty minutes. The tip of the shadow will have moved. Mark this new position. The first marker will be west of the second. Draw a line between the two markers, then run a line perpendicular to this and back towards the base of your stick (gnomon). This second line will be true north-south. The greater the distance/longer the time between marker placement, the more accurate will be your determination of north-south.

Logically, we will get a more accurate estimate if we take several hours and place a number of markers. If we do this we will observe that the shadow is longest in the morning and evening, and shortest when the sun is directly overhead. The arc plotted on the ground will be flattened rather than constant, unlike some illustrations of this method! When the shadow is at its shortest, it is on the north-south line, and the time will be local midday. The shadow will be shortest at local apparent noon (LAN), which is midway between sun-up and sun-down, so may differ from 1200 hrs. As well as determining distance, you have also made yourself a crude sundial. This can be useful in determining true local time. Some countries on the same longitude use different times. China spans several time zones but uses one official time for the whole country!

The principle is simple enough, but it can get confusing which end of the north-south line is north. In the northern hemisphere the sun (or moon) rises in the east and travels west, passing through the south. In the southern hemisphere it goes through the north.

• In the northern hemisphere the shadow always points in a northerly direction. At midday the shadow will point due north.
  
• In the southern hemisphere the shadow always points in a southerly direction. At midday the shadow will point due south.

Memorize that and solar navigation becomes much less confusing.

In the movies air-crash survivors usually undertake an epic journey back to safety. In the real world your prudent strategy is to stay near the crash site if practical. Setting up a shadow stick is a practical way to spend the time, and establishing the bearings of visible landmarks may be useful later on.

Suppose, for whatever reason, you need to travel. This decision should never be made lightly. Thanks to your shadow-stick you know what bearing you are heading out on, and that of some of the local features. But we cannot take our compass/ sundial with us! With a few modifications, we can make a portable variant.

If you have ever read about the early days of the SAS or of the Long Range Desert Group (LRDG) you will most probably have encountered to references to sun-compasses on their vehicles. In those days trying to use a magnetic compass while riding in a large lump of steel was problematic. The solution was the sun-compass.

Descriptions of how the sun-compass was used used to be hard to find. Thankfully, this is changing. The sun-compass is an ancient device, and was used by the Vikings, among others. A version was also used by some Apollo missions on the moon.

 

As you can see, some sun-compasses are very complicated or sophisticated, so not really something you can improvise. I am going to describe a less accurate variant that can be easily constructed.

In the previous blog I described how a circle of 57 mm radius had a circumference of c.360 mm. (The person who taught me this trick had 5 mm and 57 mm marked on the zipper of her jacket. I notched my penknife handle). Create such a circle on a piece of paper, back of a notebook, etc. An alternate name for a sun-compass is “shadow board”, which reminds us it can be made with a piece of plank or other flat material. A folded piece of paper will help us mark off the 45, 90 and even 22.5 degree points. Each 1.5 cm of the circumference is 15 degrees. The radius of a circle can be measured twelve times along its edge using a drawing compass, or an improvisation of one. By folding the marked points together the circle can be divided further into 24 parts, or the compass can be used further. A nail or pin can be used as the gnomon, but a sliver of wood is more likely. In fact, you do not have to mount the gnomon, just place a shadow-casting object in the centre of the circle whenever you take a reading.

All we have to do now is mark off the circle. This will be a 24 hour clockface so mark off every 15 degrees with an hour. Remember that the shadow will point due north at midday in the northern hemisphere, so mark 1200 hrs as North/0 degrees (In the south, 1200 will be South/180). Fill in the rest of the face. You might get something that looks like this:

Using this simple sun-compass is simple. Hold it level and rotate it until the gnomon shadow is over the current time. If the clocks are adjusted for daylight saving/BST or similar you will have to account for this. Remember, “spring forward, fall back”, so the shadow will be on the north-south line at 1300hs, not 1200, so you will have to subtract an hour from local time to get the time to read on the dial. Once you have your sun-compass orientated use the dial to find the bearing you want. Your portable sun-compass should agree with your base-camp shadow stick. Pick out a landmark, put away your sun-compass and walk towards the landmark. 

An alternate method is to do the same as you did with a shadow-stick. Erect a little gnomon on a board or sheet of paper and plot the tip of the shadow over the course of a day. Draw a line from the base of the gnomon across the curve where it is at its closest. To use this version you do not need to know the time. Rotate it until the tip of the shadow meets the curve. The line you drew will point north (or south if you made your sun-compass in the southern hemisphere). You must use the same height gnomon for each reading, so mount this permanently. The Ottomani version is suspended from three or four points by cord to ensure that it is level.

You may have realized that if you know the bearing of something, your sun-compass can be used as a crude sundial. Related to the methods described above is using a watch directly to navigate by the sun. Remember to adjust time for BST/DST. Substitute “1 mark” for “12 mark” in the above instructions. If your watch is digital, or you are using your phone clock, use your imagination. If you become confused as to which end of the north-south (N-S) line is north, check the local shadows. Hold a blade of grass over the watch-face and see if it casts a shadow. The one direction a shadow cannot point in the north is south. Useful to recall is “the north gets up around 3 o'clock, goes to bed around 9”. In other words, the north end of the N-S line will be in the small numbers in the morning, the higher numbers in the afternoon. (In the southern hemisphere replace the word north with south and the motto still works.) Remember, sometimes shadows are still visible even when you cannot see the sun directly. 

The basic watch method is easy to remember: midpoint between “12(/1)” and the hour hand. The specifics for each hemisphere can be difficult to remember. It may help to think that “N” for north-hemisphere looks like a “H” for “hour-hand” and that this should be pointed at the sun. A cast shadow will point in the oppositie direction to the hour hand. For the southern-hemisphere the 2 in “12” looks a little like an “S” so the 12 should be pointed at the sun. A cast shadow should point towards “6”. Hopefully that will help you use this method.

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Finding Latitude.

Currently I am reading “The Time Traveller’s Guide to Medieval England”, which is very interesting. An astrolabe is listed among the possessions of at least one wealthy merchant. This got me thinking about similar devices.

Decades ago I watched a program on someone who had spend several weeks, possibly months, in a life-raft on the open sea. Using three pencils and elastic bands he improvised a sextant and used it to measure the angle of the Pole star. Since the angle of the Pole star is equal to the latitude of the observer, he was able to sail his raft into the sea lanes, where his chance of encountering another vessel and rescue were greatest.

Here is a nice image of how such a device works. Other materials such as sticks and string could be used. This device is easily improved with a plumb-line. In the southern hemisphere you can measure the angle of the Coal Sack nebula.

Similar devices date back many centuries. If you have some cord, a kamal would be easy to improvise. Note that one example below is made from a piece of cardboard. A knot on the cord is held between the teeth and the cord pulled taunt. The bottom edge of the sight is aligned with the horizon, and the top compared with the Pole star. Different knots on the cord represented different latitudes. For example, if you wanted to sail from Alexandra to Crete you would sail north, checking your kamal using the knot corresponding to 35 degrees. Perhaps you tied that knot when you sighted Polaris another time you were on Crete. When the Pole star aligns with the top of your sight you will know it is time to start sailing west.

The cross-staff worked the same way as the kamal, as the illustrations show. It was better suited to higher latitudes. There were problems with using such a device to measure the angle of the sun, so the backstaff developed, a step towards the prisms and mirrors of the modern sextant. 

A quadrant is relatively easy to make. A number of websites show the version in the first photo. The problem with this variant is that you have to remember to subtract 90 from your reading.

It is NOT a sextant!

Easier is to use half of a typical semi-circular protractor, mount the protractor with the straight edge vertical, or mark out a piece of card or paper. When improvising navigational devices a useful thing to remember is that a circle of 57mm radius has a circumference of just under 360mm. In other words, one millimetre equals one degree. It is no coincidence that my penknife handle has three notches, one 57mm from the first, the other 5mm from the first. Thus if I make a quadrant or compass rose I can mark it in 5 degree increments. By folding paper you can accurately mark 90, 45 and 22.5 degree angles. There are several ways to draw a good circle or quarter circle with improvised means.

Or just draw around something round.

Such navigation devices can be used on the land as well as at sea. They have a long tradition of being used in deserts, exploiting the clear night skies. There are also situations where you might wish to determine the angle of a slope.

I will close with two trigonometry-based tricks:

The first can be used to determine the width of a river or road. This uses the principle of similar triangles.

Face a landmark on the far bank of the river. Turn 90 degrees and pace out a set distance, such as five paces. Place a marker (B in the illustration) and then pace out another five paces (or whatever distance you used before). A-B should equal B-C to avoid any calculations. Turn 90 degrees and head away from C. counting your paces. Every few paces look back at your landmark. When the landmark aligns with B then C-D will equal the distance between A and the landmark.

The second technique is for applications such as measuring the height of a tree or cliff. Vertical distance will equal horizontal distance when the viewing angle is 45 degrees. You can use a quadrant or clinometer for this, but you need to remember to add the height of your eye to the horizontal distance. Alternately, you can use a stick or staff and move back until it appears to be the same height as the object. Add the length of the stick/staff to the horizontal distance. You may have noticed that wood axes often have a 45 degree cut across their end. A lumberjack would sight along this, moving back until he could see the top of the trunk. Height was horizontal distance, plus the length of the axe handle.

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