Skip to main content

The arithmetic of vertical runs

Riser count, going and slope are never written. They are derived from the region, the storey pitch and one declared direction of rise.

space /B2..B1/st stair X3..X3+2600 Y2..Y2+5400 name:避難階段 stair:N form:return
npx tsx src/cli.ts runs examples/basement/main.muro
B2→B1	lift	EV	/B2/ev
B2→B1	ramp	車路	rise 3700mm	return	slope 1/7.2	going 26800mm	/B2/ramp
B2→B1	stair	避難階段	rise 3700mm	return	21 risers of 176mm, tread 300mm	going 6000mm	/B2/st
B1→L1	lift	EV	/B1/ev
B1→L1	ramp	車路	rise 3700mm	return	slope 1/7.2	going 26800mm	/B1/ramp
B1→L1	stair	避難階段	rise 3700mm	return	21 risers of 176mm, tread 300mm	going 6000mm	/B1/st
L1→R	lift	EV	/L1/ev

The 21, the 176mm, the 300mm and the 6000mm appear nowhere in the source. Here is the arithmetic that produces them.

Local coordinates​

A run is measured in t (from 0 in the direction of travel) and s (from the left of the direction of travel). The direction of rise, stair:N, fixes t, and s follows from it. Which way a turn goes is decided here.

turn: is L only when L is written; unwritten and invalid values are both R.

When no shape is generated at all​

Any of these produces no shape whatsoever. RUN01–05 / SUF04 put it into words.

  • Zero or two or more vertical-circulation declarations
  • The region is not a single rectangle
  • The level cannot be determined
  • A value other than N/E/S/W on anything but a lift, or a value other than 1 on a lift
  • form: other than straight or return
  • form:return on something other than a stair or a ramp
  • No level above (lifts excepted)
  • The entry landing consumes the full length
  • A turning run leaves no run length

A lift has a shape even with no level above — the car closes on its own level.

Entry landing and step division​

A run does not start at the edge of its region. An entry band remains at the near end, and that is where the door opens. A straight run keeps one at the far end too.

The entry band is floor, not landing. Starting a run at the edge means the stair-hall door hits a tread directly. Its depth is entry:, or ENTRY_LANDING (1100mm).

usable = length − entry            (form:return)
usable = length − entry × 2        (form:straight)

risers = max(2, ⌈rise ÷ (riser: ?? 180)⌉)
riser  = rise ÷ risers
going  = usable ÷ max(1, risers − 1)
slope  = level difference ÷ run length

riser: is an upper bound on the riser, not the riser itself. The value written decides the riser count; the actual riser is the storey rise divided by that count.

Turning​

The width is halved and an intermediate landing is placed at the far end. With turn:R the first flight runs on the left of the direction of travel, with turn:L on the right. The two flights occupy the same interval of t and differ only in s.

The split of the steps is:

k             = min(risers − 1, max(1, round(risers ÷ 2)))
landing level = FL + k × riser

round rounds a half up, so with an odd riser count the lower flight has one step more. The second flight is also geometrically reversed — the low-t side is the high one. A turning ramp puts its landing at exactly half the rise.

The landing is the remainder​

Run length, going and landing are tied by a single equation, and at most two of them can be written. What a designer wants to hold is the comfort of the going, so by default the remainder goes to the landing.

landing: written : max(LANDING_MIN, the written value)
ramp             : max(LANDING_MIN, min(width ÷ 2, (length − entry) ÷ 3))
stair            : max(LANDING_MIN, min((length − entry) − n × target going,
                                        (length − entry) − LANDING_MIN))

For the stair, n is max(1, max(k − 1, risers − k − 1)) and the target going is tread:, or TREAD_TARGET (300mm). Write landing: and the going becomes the remainder instead. Derived or written, a landing below LANDING_MIN (1100mm) is raised to the minimum.

Solve it​

/B2/st is a 2600 × 5400 rectangle. stair:N, so the length is 5400 and the width 2600, over a storey rise of 3700.

entry       = 1100                             (default)
risers      = max(2, ⌈3700 ÷ 180⌉) = 21
riser       = 3700 ÷ 21 = 176.19mm             → "21 risers of 176mm"
k           = min(20, round(21 ÷ 2)) = 11
n           = max(1, max(11−1, 21−11−1)) = 10
landing     = max(1100, min(4300 − 10×300, 4300 − 1100)) = 1300
run length  = 5400 − 1100 − 1300 = 3000
going, 1st  = 3000 ÷ (11 − 1) = 300mm
going, 2nd  = 3000 ÷ (10 − 1) = 333.3mm

The aggregate going is the tightest flight, so 300mm, and the total run length is 3000 × 2 = 6000mm. That is the CLI line, exactly.

Side by side — escalators​

The nominal width of one unit is lane:, or LANE_ESCALATOR (1200mm).

units      = max(1, ⌊width ÷ nominal⌋)
unit width = min(nominal, width ÷ units)
remainder  = (width − unit width × units) ÷ 2  split evenly between the two edges

Units alternate in direction of travel — next to an up escalator is one coming down. lane: has no effect on stairs, ramps or lifts (the count is always one).

/L1/es in examples/complex/ is 3200 wide, so:

unit 1 : t 1100…10900, s 400…1600,  up
unit 2 : t 1100…10900, s 1600…2800, down (same geometry, opposite direction of travel)

⌊3200 ÷ 1200⌋ = 2 units at 1200mm each, remainder 800 split 400 to each edge.

Aggregate values​

ValueWhat it counts
going (total horizontal run)the first unit only. Both flights of a turning run count
treadthe tightest flight represents it
slopethe steepest flight represents it

The asymmetry is what the judgements rely on — the second flight of a turning run has more steps and is therefore tighter, so looking only at the first would let a cramped flight slip past stair.proportion.

Solids​

PartShape
Landinga slab; top at the landing level, thickness SLAB_T (200mm)
Stair flightfor k risers there are k − 1 tread boards (the top step is carried by the floor above). The top of tread i is bottom + i × riser, thickness riser + TREAD_SOLID (200mm)
Ramp, escalatorone inclined slab, thickness SLAB_T
Escalator balustradetwo per unit; width min(140, unit width ÷ 8), thickness 100mm, raised 900mm above the tread surface
Lift cara box inset min(300, side ÷ 6) on all four sides. Constant height regardless of storey pitch, from FL + 60 to FL + 2400

The tilt is decided by the z values, never by the direction of travel. A down escalator tilts geometrically the same way an up one does; only the direction people move differs. Reading that one word geometrically as well is what once tilted the down unit into a mirror image, drew its arrow pointing up, and made the second unit vanish from the plan.

Neighbouring pages​