Calculations

Calculations

• Bend radius of an elbow

  The center-line radius an elbow is built with.

  pipe: the table's radius; round duct: 1.5 × diameter; rectangular duct: its width for a turn in plan, its height for a turn up or down

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

  • BimCraft
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• Elbow geometry at a corner

  The two tangent points, center and angle of the elbow where a run turns.

  θ = acos(d₁ · d₂); T = R × tan(θ ÷ 2); center = p₀ + n × R

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

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• Where runs meet

  Finds run ends that touch another run's end or lie on another run's line, to make an elbow, reducer or tee there.

  end to end when |P − Q| ≤ max(tol_a, tol_b); tee when the foot of P on a leg is within the tolerance

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

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• Elbow, reducer and tee allowances

  How much of each leg an elbow, a reducer or a tee takes.

  reducer length (duct) = max(150, max(|Δw|, |Δh|) ÷ 2 ÷ tan 15°); tee half length = max(25, 0.5 × branch + 0.25 × host)

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

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• Straight pieces between fittings

  The start and end of every straight piece along each leg, after trims, tees, valves and weld cuts.

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

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• Saving a run's definition

  The points, sizes, slope and flow kept in the run's property set.

  point = round to 3 decimals of a millimeter

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

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• Length and surface written on each piece

  The length of a straight pipe or duct piece and a duct's outside surface, written as IFC quantities.

  L = |b − a|; perimeter = π w (round), π h + 2 (w − h) (oval), 2 (w + h) (rectangle); surface = perimeter × L

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

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• Elbow written as a revolved section

  The axis and angle of the solid of revolution that an elbow is written as.

  axis at R to the side of the section; angle = θ

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

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• Flat-oval outline

  The outline of a flat-oval duct with semicircular ends.

  r = H ÷ 2; c = W ÷ 2 − r; points at c + r cos a, r sin a

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

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• Connecting ports that touch

  Joins a port to a port of another part that lies at the same place.

  connected when |p − q| < 0.6 mm

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

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• Position along a run

  How far along a run a plan point lies, and how far off the line.

  t = clamp((p − a) · d, 0, L); s = Σ earlier legs + t

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

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• Length of a run

  The length of a run's center line through its corners, with the slope applied.

  L = Σ |Vᵢ − Vᵢ₋₁|

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

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• Pipe size for a flow and a velocity limit

  The smallest pipe of a material and class whose velocity stays at or under the limit.

  V = Q ÷ (π D² ÷ 4); first size with V ≤ V_max

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

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• 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

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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

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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

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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

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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

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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

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• 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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