Additional Math Pages & Resources

Friday, June 3, 2011

Creative Units of Measure, Part IV

Today we'll finish up this week's blog series by recognizing a set of creative units known as the FFF system. The FFF designation means Furlongs, Firkins and Fortnights (distance, weight, time).
  • A furlong is 201 meters or 220 yards. It is derived from the length of a plowed furrow in an acre of farm field.
  • A firkin is 40 kg or 90 lbs and is based on the weight of a quarter cask of ale.
  • A fortnight is unit of 2 weeks, or 14 days. Here at Excel Math we get paid every fortnight, and tonight is the night!
Today, scientists and computer programmers use this measuring system to baffle and confuse each other. The system has no practical use, as these little-known units are rarely employed in common language or calculations.

This is a British sportscar known as the Jensen FF 
(but as far as I know, Jensen did not use the FFF system)

From an elementary math point of view, FFF can be used for problems that force students to focus on doing things the mathematically-correct way. The very novelty of the units makes it difficult to take short-cuts or cheat.

For example, our common measure of speed is miles per hour or km per hour.  A person can walk at a pace of 3 or 4 miles per hour. In cars we are usually driving at 30, 45 or 60 mph.

In the FFF system, 1 furlong per fortnight (FpF) is the speed of a snail who has almost fallen asleep, or a very, very slow bug.

Could we convert FpF to miles per hour? Sure. How?

We can start by learning the value of the equivalent units, like this:
  • Hours in a fortnight = 14 days x 24 hrs/day = 336 hours/fortnight
  • Furlongs per mile = 5280 feet ÷ (220 yards x 3 feet per yard) = 8 furlongs/mile
  • 1 mile per hour is the same as 8 furlongs per 1/336th of a fortnight
  • 1 furlong per fortnight is 1/8 mile in 336 hours = .125 ÷ 336 = .000372 miles per hour
  • .000372 x (5280 x 12) = 23.6 inches in an hour
I looked up the speed of ants, and learned a big black ant could travel nearly 200 inches (15 feet) in a minute. How many FpF is that?
  • 200 inches in a minute = 12000 inches in an hour
  • 12000 ÷ 23.6 = 508 FpF
We can create more convenient variants of these units, such as the microfurlong (8 inches) or microfortnight (1.2 seconds) or microfirkin (1.4 ounces).

Teachers often say, "Now that you have learned this word or concept, can you use it in a sentence?" Okay, I will give it a try. Here is the context:

Because there is a nice micro-brewery by our Excel Math editorial offices, after work I may walk across the street and have a pint of beer.

Now putting it in FFF units:

After I pick up my fortnightly paycheck (.015 fortnights from now), I will walk .5 furlongs and drink 1/72nd of a firkin.

PS - Lightning Brewery - where their methods are scientific, but their goals are artistic - does NOT employ the FFF system of measures.