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.

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 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 is based on a size 12 (a whole foot, 12 inches) and counts 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 whole foot.

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 a size smaller all the time.

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), 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 Q2)

I cover Natural Units  (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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