Calculations

Calculations

• Duct size for a flow

  A duct sized by equal friction, returned in millimeters.

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

  • BimCraft
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• Drain sizes by fixture units

  The smallest drain size that carries the fixture units reaching each sanitary run, never smaller than what flows into it.

  grow when needed nominal > drawn nominal + 1e-9

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

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• Pipe and duct schedules

  Total length and piece count per pipe size, and length and surface per duct size.

  length = Σ stored piece lengths; surface = Σ perimeter × length

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

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• Friction rate of a round duct at the velocity limit

  The pressure drop per meter used to propose a duct size when the calculation ran by velocity.

  D = √(4 Q ÷ (π v)); rate = 0.02 × (1.204 ÷ D) × v² ÷ 2

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

  • BimCraft
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• Proposed duct sizes

  The width and height proposed for each duct run that is too small or too fast.

  size for the largest flow in the run, rounded to 1 mm

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

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• 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

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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

  • BimCraft
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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

  • BimCraft
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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

  • BimCraft
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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

  • BimCraft
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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

  • BimCraft
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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

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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

  • BimCraft
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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

  • BimCraft
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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

  • BimCraft
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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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• 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

  • BimCraft
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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

  • BimCraft
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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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• Link matrix through both files' map positions

  The matrix from the linked file's millimeters to the open model's, through the map grid both are placed on.

  m = S(host unit) × host map⁻¹ × S(1 ÷ host map unit) × S(link map unit) × link map × S(1 ÷ link unit)

  Placing a linked model model-links.js

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• Link matrix from two pairs of points

  The turn and move that carry two picked points of the linked model onto two picked points of the open one.

  a = atan2(h₁ − h₀) − atan2(l₁ − l₀); t = h₀ − R(a) × l₀

  Placing a linked model model-links.js

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• The same change in the scene

  Carries a link matrix between the file's millimeters and the viewer's scene.

  A = F × m × F⁻¹; m = F⁻¹ × A × F

  Placing a linked model model-links.js

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• Saving the link matrix

  The matrix written into the model as text.

  entry = round(v × 10⁹) ÷ 10⁹

  Placing a linked model model-links.js

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• Sheet and scale

  The paper size, the drawing's extent and the scale it prints at.

  fits when W ÷ r ≤ room width and H ÷ r ≤ room height

  Plan as a vector PDF model-pdf.js

  • BimCraft
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• Plan millimeters to the sheet

  The scale factor and offsets that place the plan on the page.

  k = 1 ÷ ratio; paper = offset + plan × k; points = paper × 72 ÷ 25.4

  Plan as a vector PDF model-pdf.js

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• Coordinate written to the PDF

  How a path coordinate in points is turned into text.

  text = Number(v.toFixed(6))

  Plan as a vector PDF model-pdf.js

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