Calculations

Calculations

• Reading a typed slope

  Turns '1/4"/ft', '2%', '1:50' or '0.02' into rise per run.

  inch per foot ÷ 12; percent ÷ 100; 1 ÷ n

  Pipe and duct runs: layout, lengths and sizing mep-ui.js

  • BimCraft
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• Schedule totals

  The total length, piece count and duct surface shown under the pipe and duct schedules.

  ft² = mm² ÷ 92903.04

  Pipe and duct runs: layout, lengths and sizing mep-ui.js

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• Runs handed to the takeoff

  The plan length, pitch and surface height of pipe and duct pieces passed to TakeoffCraft.

  pitch = atan(slope) × 180 ÷ π; heightFt = perimeter ÷ 304.8

  Pipe and duct runs: layout, lengths and sizing mep-ui.js

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• Weighted sound reduction index

  Rw and the adaptation terms C and Ctr from sixteen third-octave sound reduction values.

  highest shift s with Σ max(0, ref + s − R) ≤ 32; Rw = ref₅₀₀ + s; C = round(X_A − Rw)

  Sound insulation ratings and the mass law insul.js

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• Spectrum adaptation sum

  The A-weighted level difference for a reference spectrum.

  X_A = −10 lg Σ 10^((Lⱼ − Rⱼ) ÷ 10)

  Sound insulation ratings and the mass law insul.js

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• Weighted impact sound level

  Ln,w and the adaptation term CI from sixteen third-octave impact levels.

  lowest shift s with Σ max(0, L − (ref + s)) ≤ 32; Ln,w = ref₅₀₀ + s; CI = round(10 lg Σ 10^(L ÷ 10) − 15 − Ln,w)

  Sound insulation ratings and the mass law insul.js

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• Mass law

  The sound reduction of a single-leaf wall from its mass per area and the frequency.

  R = 20 lg(m × f) − 47

  Sound insulation ratings and the mass law insul.js

  • BimCraft
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• Critical frequency

  The frequency at which a panel's bending wave matches the speed of sound in air.

  fc = c² ÷ (2π h) × √(12 ρ (1 − ν²) ÷ E), c = 343

  Sound insulation ratings and the mass law insul.js

  • BimCraft
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• Mass-law reduction by octave band

  The mass-law value in the octave bands from 125 to 4000 Hz, up to half the critical frequency.

  m = ρ × h; R(f) for f ≤ fc ÷ 2

  Sound insulation ratings and the mass law insul.js

  • BimCraft
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• Replacement years, cost and present value

  Every replacement in the study period with its cost, and the totals by year and by part.

  t = t₀ + k × life; cost = q × c × (1 + i)^t; PV = cost ÷ (1 + r)^t

  Replacement schedule and cost over the building's life lifecycle.js

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• Replacement schedule as CSV

  The schedule and the year-by-year costs written as text.

  money = round(x × 100) ÷ 100; carbon = round(x × 10) ÷ 10

  Replacement schedule and cost over the building's life lifecycle.js

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• Quantities of the building's parts

  Window area, door counts, exterior wall area, room finishes, roof area and stairs taken from the model.

  wall = Σ perimeter ÷ 1000 × height − openings; window = w ÷ 1000 × h ÷ 1000; quantity = round(q × 100) ÷ 100

  Replacement schedule and cost over the building's life lifecycle-model.js

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• Age of an installed item

  Years between an item's install date and today.

  age = (today − installed) ÷ (365.25 days)

  Replacement schedule and cost over the building's life lifecycle-model.js

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• Quantities of the building services

  Equipment by class, meters of pipe and duct, and an estimate of the wiring.

  pipe = round(Σ |pᵢ − pᵢ₋₁| ÷ 1000, 2); wiring = round(Σ nearest distances ÷ 1000 × 1.25, 2)

  Replacement schedule and cost over the building's life lifecycle-model.js

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• Carbon per unit of each part

  The embodied carbon of one unit of a part, from the model's carbon totals.

  kg per unit = Σ carbon of the part's elements ÷ quantity

  Replacement schedule and cost over the building's life lifecycle-model.js

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• Reading WAV samples

  The first channel of a WAV file as numbers between −1 and 1.

  x = sample ÷ 2^(bits − 1)

  Room acoustic measures from an impulse response metrics.js

  • BimCraft
  32-bit in part

• Decay time from a line fit

  A decay time from the slope of the least-squares line through part of the decay curve.

  slope = (m Σ t d − Σ t Σ d) ÷ (m Σ t² − (Σ t)²); T = 60 ÷ −slope

  Room acoustic measures from an impulse response metrics.js

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• Decay curve, clarity, definition and center time

  The energy decay curve and the measures read from it.

  curve = 10 lg(∫ₜ p² ÷ ∫₀ p²); C = 10 lg(early ÷ late); D50 = early ÷ total; Ts = Σ t p² ÷ Σ p²

  Room acoustic measures from an impulse response metrics.js

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• Predicted against measured

  The difference between a predicted and a measured value in each band, against the just-noticeable difference.

  within when |predicted − measured| ≤ JND

  Room acoustic measures from an impulse response metrics.js

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• Circle of an arc

  The center, radius, angle and length of the arc between two points with a bulge.

  θ = 4 atan(b); h = b c ÷ 2; R = ((c ÷ 2)² + h²) ÷ (2 |h|); length = R |θ|

  Curved walls model-arcs.js

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• Chord of an arc of a given length

  The straight distance between the ends of an arc of a given length and bulge.

  chord = len × sin(θ ÷ 2) ÷ (θ ÷ 2)

  Curved walls model-arcs.js

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• Arc height and bulge

  How far the arc's middle stands off its chord, and the bulge for a typed height.

  height = −b × c ÷ 2; b = −2 h ÷ c

  Curved walls model-arcs.js

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• Arc through three points

  The bulge of the arc from a through p to b.

  d = 2 (a_x (p_y − b_y) + p_x (b_y − a_y) + b_x (a_y − p_y)); bulge = tan(θ ÷ 4)

  Curved walls model-arcs.js

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• Chords of an arc

  The points between an arc's ends when it is drawn or saved as straight pieces.

  n = max(1, ⌈|θ| ÷ step⌉); point = C + R (cos f, sin f)

  Curved walls model-arcs.js

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• Points along and off a wall

  A point at a distance along a wall and an offset to its left, and the reverse, for straight and curved walls.

  curved: p = C + (R − off × sg) (cos φ, sin φ), φ = a₀ + sg × s ÷ R

  Curved walls model-arcs.js

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• Where an opening sits in a curved wall

  The position and angle of a door or window in the wall's own axes, square to the wall at the opening's middle.

  O = at(off + w ÷ 2) − T × w ÷ 2; angle = atan2(T) − chord angle

  Curved walls model-arcs.js

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• Offset of an opening read back

  The distance along a curved wall of an opening, from the matrix that places it.

  offset = s(middle) − w ÷ 2

  Curved walls model-arcs.js

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• Opening body in a curved wall

  The four corners of the body that cuts an opening through a curved wall, with jambs along the radius.

  half = w ÷ R ÷ 2; outer radius = r ÷ cos(half)

  Curved walls model-arcs.js

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• Axis curve saved for a curved wall

  The circle and its two trim points written as the wall's axis.

  circle of radius R about the center in the wall's axes, trimmed from (0, 0) to (chord, 0)

  Curved walls model-arcs.js

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• Profile with arc edges

  The closed outline of a curved wall written with true arcs (IFC4) or chords (IFC2X3).

  arc edge = start, middle of the arc, end

  Curved walls model-arcs.js

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• Height of a column

  The height a column is built with: up to its top level plus an offset, else its fixed height.

  h = top elevation − own elevation + offset

  Columns: height and quantities model-columns.js

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• Cross-section area and volume

  The quantities written on a column.

  area = π (w ÷ 2)² or w × d; volume = area × h

  Columns: height and quantities model-columns.js

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• Sizes saved with a column

  The width, depth, angle and heights kept in the column's property set, which is what is read back.

  Columns: height and quantities model-columns.js

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• Columns following a level

  Rebuilds columns whose height no longer matches their levels.

  rebuild when |stored − wanted| > 0.5 mm

  Columns: height and quantities model-columns.js

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• Area of an outline

  The signed area of a polygon.

  A = ½ Σ (xᵢ yᵢ₊₁ − yᵢ xᵢ₊₁)

  Drawn floors: outline, openings and quantities model-floors.js

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• Perimeter of an outline

  The total length of the outline's edges.

  P = Σ |pᵢ₊₁ − pᵢ|

  Drawn floors: outline, openings and quantities model-floors.js

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• Do two edges cross

  A yes or no on whether two segments properly cross.

  cross when o(a, b, c) × o(a, b, d) < 0 and o(c, d, a) × o(c, d, b) < 0

  Drawn floors: outline, openings and quantities model-floors.js

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• Is the outline usable

  Refuses an outline with fewer than 3 corners, one that crosses itself, or one with almost no area.

  refuse when |A| < 10 000 mm²

  Drawn floors: outline, openings and quantities model-floors.js

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• Is a point inside the outline

  The even-odd test used to check that an opening lies in its floor.

  Drawn floors: outline, openings and quantities model-floors.js

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• Saving and reading the outline

  The outline's points written as text in the file's length unit, and read back.

  text = round(x ÷ unit, 3) , round(y ÷ unit, 3)

  Drawn floors: outline, openings and quantities model-floors.js

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• Perimeter, area and volume written on a floor

  The slab quantities, gross and net of the openings.

  net area = A − Σ |hole|; volume = area × thickness

  Drawn floors: outline, openings and quantities model-floors.js

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• Flights and landings of a ramp

  Where each flight and landing starts and ends along the ramp, and at what height.

  n = max(1, ⌈rise ÷ maxRise − 1e-9⌉); flight run = rise ÷ n × slope; steep when slope < 12 − 1e-9

  Ramps: flights, landings and quantities model-ramps.js

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• Rise of a ramp

  The height a ramp climbs: to its top level, else the rise typed.

  rise = top elevation − own elevation

  Ramps: flights, landings and quantities model-ramps.js

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• Flight slope, length and volume

  The slope angle, sloped length and volume written on each flight.

  slope = atan(Δz ÷ len); length = √(len² + Δz²); volume written = length × width × t

  Ramps: flights, landings and quantities model-ramps.js

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• Values saved with a ramp

  The start point, sizes, slope and the rise and run used, kept in the ramp's property set.

  required slope = atan(1 ÷ slope)

  Ramps: flights, landings and quantities model-ramps.js

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• Ramps following a level

  Rebuilds ramps whose rise follows a level that moved.

  rebuild when |rise − rise used| > 0.5 mm

  Ramps: flights, landings and quantities model-ramps.js

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• Grid lines by spacing

  The ends of numbered and lettered grid lines from a count, a spacing or list of spacings, an origin and an angle.

  xᵢ = xᵢ₋₁ + spacing; P = origin + R(angle) × (x, y)

  Grid lines model-grids.js

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• Where grid lines cross

  The crossing points of every pair of grid lines, for snapping.

  den = r × s; t = (q − p) × s ÷ den; point = p + t r

  Grid lines model-grids.js

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• Grid lines an elevation shows

  The lines that run within 30° of a view's direction, and where they sit across the view.

  kept when |e · d| ÷ |e| ≥ 0.866; x = a · right

  Grid lines model-grids.js

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• Is the grid rectangular

  A yes or no that decides the grid's type in the file.

  parallel when |d₁ × d₂| < 1e-6; square when |u · v| < 1e-6

  Grid lines model-grids.js

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