More Weird units

Working on the assumption that you are a little bit interested in the use of number, this page addresses units you might well use or find in use, that need some explanation.

Cooking, food and power

 A gas oven in the UK and across the Commonwealth may be marked in apparent single units. The conversion is one ‘gas mark’ unit for each 25ºF, working from 1 at 275ºF to 9 at 475ºF. I’d recommend an oven thermometer if it matters to you. Convert F to C by the usual C= 5(F-32)/9. Gas Mark X is also called Regulo Mark X. Your great-grandmama will remember this.

French ovens use Thermostat readings, where 1 means 30ºC, going up in units of 30º, so Th 6 is 180ºC. German ovens step in mainly twenties; Stufe 2 is 160ºC and Stufe 8 is 280ºC.

A Barrel varies: 31 gallons for beer, 40 for whiskey and 42 for petroleum. Other barrels are 31.5 gallons. A typical ‘oil drum’ is not  a barrel, it is a 55 gallon drum, not a standard measure, even though you might think so. And US barrels are different from Imperial ones.

Wheat, corn and barley are measured in bushels, which is a volume, 2150.42 cubic inches US. Typical weights are 32-34 pounds for oats, 48 lbs for barley, 56 lbs for corn and 60 for wheat. A bushel is about the size of a large basket you'd be comfortable carrying any distance. Imagine one to be around half a metre diameter and around 20cm deep. I could write a page just of old measures of food in volume.

A Horsepower is 745.7 Watts, though I learned 746 Watts, being 550 foot pounds per second, produced by an averaging and rounding of 33000 foot-pounds per minute from a working horse across a four-hour shift. If you research this, you’ll find James Watt’s name included.

Shoe sizes:
UK units are based on a size 12 (a whole foot, 12 inches) and count back-wards in barleycorn units, three per inch. So a size 9 is 11 inches. A child’s size zero is a hand (4 inches, 10.16cm), up by an inch each three sizes to 13½ at 8½ inches; the next half size up is an adult size 1, but that builds in a disagreement, since working back from size 12 being 12 inches says a size zero is 8 inches, not the 8.33 described, which makes a size 13 the correct whole foot, not the size 12 where we were supposed to start. Confusing; that is why 'kids' sizes' often don't agree with 'adult sizes'; the foot-long foot should be a size 13.

American sizes are very similar, being one barleycorn different and getting the 12 for 12 right. (Which says to me a man did this, size 12 foot). American women’s shoes are 1.5 sizes different from the men - a man’s 8½ is a woman’s 10. Kiddies' shoes continue to be 1/3 inch different from the British measurement, ending at 13. So US sizes are a third of an inch, a size, different all the time. If you're British, the American feet are bigger by a size.

European sizes are also based on thirds; two/thirds of a centimetre between point sizes, called a Paris point (perhaps pronounced French-style, as Paree pwahn). 120mm on a child’s foot starts size 20 and so 180mm starts size 29. Size 30 and UK 11½ are very close, as are size 23 and size 6. On adults, 220mm of foot matches the start of size 35; size 37 matches a US 5 very well; 300mm is where size 47 begins. 305mm is the end of US size 13 but the start of UK size 13, being a foot long, still in the range of size 47, which ends at 306.66mm. Americans also have ‘athletic’ sizes, which span a greater range across the same ‘sizes’; the nines are the same, a standard 2 is an athletic 3 and a standard 15 is an athletic 14.

Mondopoint takes the Euro size, adds ten and multiplies by five, so a Euro 36 moves to a 230. Working the other way, read the 3 figure number, divide by ten, double that and deduct ten; your UK size 10 is a Euro 44 and  Mondo 280. Actually, while much quoted to me, that conversion fails unless you’re a size 4-7; guys should add/subtract 11-13, not 10.  Mondopoint is an inter-national sizing system, ISO 9407. A size (says Wikipedia) labelled 280 or possibly 280/110 will fit a foot of length 280 mm and width 110mm. The other systems describe the shoe (the 'last' used to make the shoe), not the targeted foot size. The wikipedia page underlines that a shoe size is to fit a range of length, which emphasises how you might feel you are a ‘5 or a 6’, a ‘9 or a 9½’, and similar expressions.

1.  Which gas mark is nearest 150ºC? 400ºF?

2.  Does the French Th8 = Stufe 6? What’s that in Celsius? Can you write a formula converting Stufe (n) to Centigrade?

3.   How many litres in a 55 gallon drum, to 3 sig.fig??

4. Your new (gir) friend wears UK size 5 (she says); what size is she likely to wear in Euro and US units? Your new (boy) friend wears Euro 45; what size is this in UK and US units?

I wrote a lot more about weird units in the essay section. 166 - Dress Sizes.. I have written (somewhere) a lot more about shoes (above) and about needles (CNY Maths Q3)

I cover Natural Units  (which is Sixth Form content) but I have filed it (201711) in here, Extension Work.

  1.  is 150ºC, 6 is 400ºF and 204ºC; 9 is 246ºC

  2. Yes: both are 240ºC, close to gas Mark 9.

  3. 55x4.54609 = 250 litres, 250.03495 is too precise to match the use of a drum.

  4. UK 5 is probably 8.5 US women, 38 Euro and 240 Asian/Mondopoint. Euro 45 is probably a UK 10, a US 11.5 (just might be an eleven) and an Asian 285 or 290.
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