Flying Metrics
Robert C.
1 4 5 16 3 8 7 …
Measuring
◉ is comparing (to a unit)
◉ and is for comparing!
◉ communicate the result: a number
◉ → number systems crucial
Number system bases
◉ 7
Mon Tue Wed Thu Fri Sat Sun
◉ 10
◉ 12
◉ 20
Four score and seven years ago…
◉ 28 = 4×7
lunar cycle(s)
◉ 30
month
◉ 60
minutes, seconds, …
Quirky
◉ … ten eleven twelve thirteen … nineteen twenty twenty-one …
twenty-nine
◉ 99 = quatre-vingt-dix-neuf = 4×20+10+9
◉ 125 = hundert fünf-und-zwanzig = 100 + 5 + 20 (but not neuf-dix!)
◉ (still not as bad as JavaScript)
◉ (and why month-day-year ??)
Computing is base 10
Fractions are out
except perhaps very simple ones: 1/2, 1/3, 3/4.
we write 3.1416 not 22/7
The Metric System
Factors are base 10
◉ easy computations
◉ factors 1, 10, 100, 1000
◉ prefixes of factor 1000: pico nano micro milli — kilo mega giga tera
◉ quantities are round numbers
2m:
10A:
1l:
The Imperial System
The Imperial Apology
◉ Supposedly "more human"
◉ but what is a gallon?
◉ how to deal with electricity?
◉ question of reproducibility
Full of weird numbers
◉ 0º F cold brine
◉ 22 yards in a chain
◉ 3 feet in a yard,
◉ 32º F freezing point of water
◉ 6 teaspoons in a floz,
◉ 100º F core human body
temperature (fever?)
◉ 6.2288 gallon in a
cubic foot,
◉ 128 floz in a gallon,
◉ 8 gallons in a bushel
◉ 212º F boiling point of water
◉ 10 chains in a furlong
◉ 640 acres in a square mile
◉ 12 inch in a foot,
◉ 1760 yards in a mile,
◉ 14 pounds in a stone,
◉ 5280 feet in a mile,
◉ 16 cups in a gallon,
◉ 43'560 square feet in an acre
Other quirks
◉ nautical miles
◉ UK gallon, US gallon, troy ounce, long ton, short ton, …
◉ Fahrenheit is still official in the Bahamas, Belize,
the Cayman Islands, Palau,
◉ and the USA.
Difficult to compute
1 4 5 16 3 8 7 …
16
1/4" 5/16" 3/8" 7/16" 1/2"
9/16" 5/8" 11/16" 3/4" 13/16"
7/8" 15/16" 1"
6 7 8 9 10 11 12 13 14 15 16 17
the Metric System
is more elegant,
BUT…
It is full of half-metric units
◉ one very strange base unit: the second
(60x60x24 in a day, and 24 h clocks but 12h language)
◉ kWh (1000 J/s × 60×60 seconds)
◉ calorie (energy to heat 1gram of water by 1ºC, = 4.1868J)
◉ horsepower (lift a weight of 75kg by 1m in 1s = 0.745kW)
◉ km/h (why not m/s? 50km/h ≈ 15m/s)
kg for force instead of N
W for light instead of Lumen
So why do we still have
Imperial units
on the planet?
5 reasons
1. Divisors
◉ 10 = 2 × 5
◉ but when did you last cut a pizza in 5 parts?
◉ or tiled the floor in pentagons?
◉ Imperial has a factor 3: 12 inch in a foot, 3 feet in a yard
2. Pegs in your brain
3. It's in the language
◉ inch forward
◉ go the extra mile
◉ not an ounce of common sense
4. Move Posts
5. USA
◉ all factories must re-tool
◉ but is that a real argument?
◉ 415g cans?
47.5g chocolate bars?
A Compromise? (dream on…)
◉ change the names: cm → inch, metre → yard
◉ compute in base 12: all calculators in the bin! (sorry, trash)
and need to design two new digits.
(e.g. dix and elf:
◉ use the metric concept of unit factors
◉ go for 400 grades
…
Flying
what a mess ! !
◉ height and altitude in feet
◉ distance in nautical miles
◉ visibility in km
◉ outside air temperature in ºC (icing!)
◉ headings in degrees
◉ air pressure in hPa (hectoPascal)
◉ wingspans (ground manoeuvering) and runway lengths in metres
◉ fuel capacity in gallon or litre (dangerous!)
◉ radio language: ? (dangerous!)
Did I get used to it?
◉ Yes.
◉ well…
◉ because I only need a few relatively unrelated concepts
◉ altitude in feet does not mix with distance in nautical miles
◉ fuel flow does not mix with anything else at all in daily life
Is it a Mess?
◉ I fill the 24 gallon tank from the pump that dispenses in litres
◉ fuel flow on the Tecnam is 18l/h and on the Piper Warrior 10gal/h
◉ heading calculations are difficult
(multiples of 90 not 100; what is inverse of 345º?
should be 145º but is 165º
◉ 6 minute rule: because 6 minutes is 1/10th of an hour
Prejudice against aeronautics
◉ electricity :-D
◉ civil engineering :-)
◉ thermodynamics :-|
◉ flow of compressible fluids :-(