Angle

Decided: angles are measured in turns, written as dozenal fractions.

Why: it matches the clock: hand 1 turns once a day, so the time of day in days is the angle of the hand (0;1 turn = one chime on the dial). The common angles become round: right angle 0;3, 30° is 0;1, 60° is 0;2, 45° is 0;16. Degrees written in dozenal digits work (360° = 260°) but stay awkward (90° = 76°, 45° = 39°), because 360 is a decimal-era choice.

Advantage: common angles are single digits, and a clock hand's angle is the time of day.

Decided: the turn's symbol is tu (eg a right angle is 0;3 tu).

Why: it follows the first-two-letters rule. "t" alone was considered, but it's the tonne's symbol, and no symbol may clash with an SI one.

Advantage: it follows the symbol rule and doesn't clash with the tonne.

Turn Degrees (dec) Note
1 360 full turn
0;6 180 half turn
0;3 90 right angle
0;2 60
0;16 45
0;1 30 one clock mark
0;01 2.5
0;001 0.208 finest everyday step
  • Compass bearings as three digits of a turn: 000 north, 300 east, 600 south, 900 west
    • between them: 160 north-east, 460 south-east, 760 south-west, X60 north-west
    • a bearing and a time of day are the same three digits: the time is in thousandths of a day, the bearing in thousandths of a turn, so at 600 hand 1 points at 600 on the dial
    • in the northern hemisphere the sun's bearing is roughly the time of day: 000 at midnight, 600 at noon (so a clock can find north - see Analogue clocks)
  • Latitude and longitude in turns: one navis (930 p) along a meridian is about 0;0001 turn of latitude
  • Three digits act as "more degrees": 1,000; steps per turn (1,728 dec, 0.208° each), and every common angle is a round whole number: right angle 300, 60° 200, 45° 160, 30° 100. A right angle of 1,000; adds nothing over this, since 4 already divides 100;.
  • 1 turn = 2π radians = 6;34941697 radians
Compass points in turns A compass rose with north at the top. Bearings are three dozenal digits of a turn: north 000, north-east 160, east 300, south-east 460, south 600, south-west 760, west 900, north-west X60. The ring has twelve marks of 0;1 turn (100) each. 100 200 400 500 700 800 X00 E00 N 000 NE 160 E 300 SE 460 S 600 SW 760 W 900 NW X60
Compass points as bearings in turns: the cardinal points are 000, 300, 600, 900 and the points between them 160, 460, 760, X60. Each of the twelve marks is 0;1 turn (100).

Rule of thumb: a hand held at arm's length. Hands and arms grow together, so this works for most people, adults or children. Turns are given in thousandths, the bearing digits.

At arm's length Degrees (dec) Turns Sky turns in about
Sun or Moon 0.5 0;0025 (2;5) 2;5 moments
Little finger, width 1 0;005 (5) 5 moments
Thumb, width 2 0;00X (X) X moments
Three middle fingers 5 0;02 (20) 20 moments
Fist, across the knuckles 10 0;04 (40) 40 moments
Index to little finger, spread 15 0;06 (60) 60 moments (0;6 ch)
Thumb to little finger, spread 20-25 0;08-0;0X (80-X0) 80-X0 moments
  • Fist and spread hand are round numbers of turns: 0;04 and 0;06 are exactly 10° and 15°
  • The sky turns once a day, so it turns 0;001 turn (one bearing step) per moment: the sun and stars move about one fist every 40 moments (0;4 chime). Exact on the celestial equator, slower near the poles
  • The same digits come out in today's minutes only by coincidence: a dozen moments is 10 minutes, so 40 moments is 40 minutes and 60 moments an hour - but 45 moments is about 44 minutes, not 45