Fuel Mixing, Units, Ratios,
Volumes, Liquids & Weights
2012 Apr 8 More than you ever wanted to know about fuel mixing
and units, thanks to Glen Boyd
Caution: This may be more than you ever wanted to know about the
subject!
Spreadsheet guru
Glen Boyd started writing a quick & dirty sheet for calculating gas
mixes for his own use. With a basic understanding of US &
UK (Imperial) gallons, liters, and a
Metric Converter calculator, he wanted to work out the conversion
factors from, as he says, “first principles” perspective. But what was
the formal definitions of both gallons?
Some Googling revealed
the conversion process to be surprisingly convoluted. US &
UK gallons are basically apples and
oranges because they’re defined by different units: one with cubic
inches (US), the other in pounds of water. (see below "Liquid Volumes")
Glen also made some observations
about a handy little program (downloadable here on footflyer) called
Convert that may have some
small errors. Glen wrote a spreadsheet to do his own
liquid volume
conversion, GasOilMix.xls. He shares
his observations
about Convert's Volume tab:

It does not have UK
Quarts or UK Cups

It uses a value of
4.546092 liters per
UK
gallon. According to the Wikipedia article on “Gallon” (2012/Mar/27), as
of 1985 the UK
gallon was redefined to be the same as the Canadian (Imperial) gallon:
4.54609 liters.

Some discrepancies
between Josh’s factors & mine. I think they’re all due to our different
values for liters (above). (“VolumeConversions.xls”)
This, by the way, is why I'm glad that Glen is
handling most of the USPPA scoring work!
Liquid Volumes: WAY beyond Paramotor Fuel Mixing
This all started when I had to mix
my first batch of PPG gas in Florida last November; I’m Canadian, eh?
Personal opinions of the Metric System aside, calculations involving
multiples of ten can make some results more intuitive – as opposed to,
for example, 3.785411784, 4.54609, 8, 16, 20, 128, and 160. Of course,
with a handydandy measuring container like “Ratio Rite” (thank you Mike
Britt), no thinking is required. But how does it calculate ratios?
Here’s an example. Say you have 2.5
gallons (US or UK), or for the sake of argument, 10 liters of gas. Your
PPG motor requires a 50:1 gastooil mix. How much oil must be added? If
you’re dealing with gallons, it will be X ounces (oz); with liters it
will be X milliliters (ml).
2.5 US Gallons:
 2.5 gallons x 128 oz/gallon = 320 oz
 320 oz / 50 = 6.4 oz of oil
2.5 UK Gallons:
 2.5 gallons x 160 oz/gallon = 400 oz
 400 oz / 50 = 8 oz of oil
10 Liters:
 10 liters x 1000 ml/liter = 10,000 ml
 10,000 ml / 50 = 200 ml of oil
A pocket calculator with builtin
unit conversions provides some basics. But those factors are just cold,
impersonal (and sometimes approximate) numbers. Like the synthetic charm
of a receptionist who has little insight into what’s actually going on
behind the scenes.
To fly is to buy gas, often by the
gallon, a liquid gallon; UK (Imperial) or US, that is. Its major
subunits are quarts (4) and pints (8), both north and south of the 49th
parallel (Canada/US border). There’s also a US dry gallon, but that’s
not very useful at gas pumps.
A US gallon contains 128 ounces; a
UK gallon, 160. Also, a cup (in both systems) equals 8 ounces. But now
things start to get a bit fuzzy visàvis the PINT.
The aptly named quart equals
onequarter of a gallon, so a US quart equals 32 ounces; a UK quart, 40.
Ipso facto, a US pint equals 16 ounces and a UK pint, 20. No doubt you
saw this coming; it means that a US pint contains 2 cups; a UK pint, 2.5
cups. Somebody couldn’t leave bad enough alone.
The plot thickens. At first blush
one might deduce that one gallon is exactly 80% of the other (128 /
160), or vice versa, 125% (160 / 128). Not so; the approximate factors,
are 83.267% and 120.095%, respectively. Yes, this is “New Math”, but it
began 300 years ago.
Let’s start with the present then
work back. The current definitions of gallons are:
one UK Gallon = the volume of 10 pounds of water at 62 °F
one US Gallon = 231 cubic inches
How? Why? Who could think of such
things?
Wine trade was the culprit. No doubt
the defining powersthatwere spent many a long evening in the wine
cellar defining and redefining their definitions with extensive
laboratory tests. They finally decided that an appropriate volume would
be contained in a cylinder six inches high and seven inches in diameter.
(There is no record regarding this vessel’s subsequent use in public
wine tastings.) Yes, but what about 231 cubic inches?
The volume of a cylinder equals its
height (H) multiplied by the area of its base. The base is a circle, so
its area equals Pi multiplied by the square (a value multiplied by
itself) of the radius (R, half the diameter). Thus, a cylinder’s volume
equals H x Pi x R x R; in this case, 6 x Pi x 3.5 x 3.5. This equals
73.5 x Pi cubic inches. Yes, but what about 231 cubic inches; and Pi?
Pi is the ratio of a circle’s
circumference to its diameter. Today its value is known to a gazillion
decimal places, starting with 3.14159. That means a 6 x 7inch
cylinder’s volume equals (approx.) 230.907 cubic inches – close, but no
cigar. Way back then in the wine cellar one of the oenologists
remembered that Pi was approximately 22 / 7 (3.14286 – accurate to only
two decimals). Grabbing a charcoal stick he scrawled on a wine barrel’s
buttend an equation that made history: “73.25 x 22 / 7 = 231”. To date,
this is how the US defines a gallon: 231 cubic inches. (This seems quite
practical since it’s a nobrainer to calculate a tank’s dimensions for a
given volume.)
The British had a hangup with the
metric system and decided that their gallon would be based on the volume
of 10 pounds of water (at 62 °F). Tank design is now slightly more
complicated. How does one calculate the linear dimensions for a given
volume if the volume is amorphous? Anyway, the UK gallon was defined in
1976 as 4.546092 liters. In 1985 the Canadian value of 4.54609 liters
was adopted.
Great, US and Canadian gallons can’t
be directly compared; it’s necessary to first convert them to liters.
That’s why one US gallon is (approx.) 83.267% of a UK gallon, rather
than 80% exactly; etc.
If an ounce contained the same
volume in both systems there wouldn’t be a problem. But not only are the
two ounces different in size, they’re also defined in different units. A
US ounce is 231/128 (~1.8047) cubic inches; a UK ounce is 4.54609/160
(~0.0284) liters – apples and oranges. So now liters are involved.
Moving right along, one liter equals
one thousand cubic centimeters. There are 2.54 centimeters (exactly) in
one inch. One US gallon equals 3785.411784 cubic centimeters exactly:
(231 x 2.54 x 2.54 x 2.54). Since one liter equals one thousand cubic
centimeters (cc), then 3785.411784 cc equals 3.785411784 liters. One UK
gallon (by definition) equals 4.54609 liters. Thus the ratio of a US
gallon to a UK gallon is: 3.785411784 / 4.54609 ~ 0.83267; and vice
versa, 4.54609 / 3.785411784 ~ 1.20095
Glen Boyd,
April 05, 2012
