Calculations

Calculations

• Sample pieces of a room's surface

  Cuts each triangle of the room's shell into small pieces and starts one ray from each.

  k = ⌈longest edge ÷ 0.25 m⌉; k² pieces of area (triangle area ÷ k²); start = piece center + 1e-4 m × normal

  Heating and cooling loads per room energy-bim.js

  • BimCraft
  64-bit

• What lies beyond a bounding element

  Whether a piece of the room's surface faces another room, the ground or the outside.

  probe = start + normal × (farthest crossing + 0.25 m)

  Heating and cooling loads per room energy-bim.js

  • BimCraft
  64-bit

• Window and door areas

  Sets each window's and door's area to its own width times height and takes the difference from its wall.

  A = OverallWidth × OverallHeight (in m); wall area = wall area − (A − sampled area)

  Heating and cooling loads per room energy-bim.js

  • BimCraft
  64-bit

• U-value from material layers

  The U-value of an element from the thickness and conductivity of its layers.

  U = 1 ÷ (Rsi + Σ dᵢ ÷ λᵢ + Rse); Rsi, Rse = 0.13, 0.04 sideways; 0.10, 0.04 upward; 0.17, 0.04 downward

  Heating and cooling loads per room energy-bim.js

  • BimCraft
  64-bit

• Heating load, annual energy and cooling peak

  Each room's design heat loss, its degree-day year and its cooling peak.

  H_vent = 0.335 × n × V; heat = H_out·ΔT + H_ground·ΔT_g + H_vent·ΔT; annual kWh = (H_out + H_vent + H_ground × ΔT_g ÷ ΔT) × DD × 24 ÷ 1000

  Heating and cooling loads per room energy-bim.js

  • BimCraft
  64-bit

• Degree-days from a CSV file

  The sum of the degree-day column of a CSV file, for a year.

  total = Σ of the last numeric cell of each row

  Heating and cooling loads per room energy-bim.js

  • BimCraft
  64-bit

• A number in the file

  A value written into the input file as text.

  text = round(x × 10ᵈ) ÷ 10ᵈ, d = 4 unless stated

  Energy model input file (IDF) and its results energy-ep.js

  • BimCraft
  64-bit

• Triangles grouped into planes

  The triangles of a room's shell sorted into the flat faces they belong to.

  key = (round(1000·n), round(1000·d)), n = unit normal, d = n · A

  Energy model input file (IDF) and its results energy-ep.js

  • BimCraft
  64-bit

• Outline of a face

  One polygon from the triangles of a flat face.

  Energy model input file (IDF) and its results energy-ep.js

  • BimCraft
  64-bit

• Which way a polygon faces

  The normal of a polygon, used to order its corners counter-clockwise seen from outside.

  n = Σ ((yᵢ − yⱼ)(zᵢ + zⱼ), (zᵢ − zⱼ)(xᵢ + xⱼ), (xᵢ − xⱼ)(yᵢ + yⱼ))

  Energy model input file (IDF) and its results energy-ep.js

  • BimCraft
  64-bit

• Construction by U-value

  The thermal resistance written for a wall, roof or floor that has no layer build-up.

  R = max(0.001, 1 ÷ U − Rs), Rs = 0.17 wall, 0.14 roof, 0.21 floor

  Energy model input file (IDF) and its results energy-ep.js

  • BimCraft
  64-bit

• Mean U-value of a room's walls, roof and floor

  The area-weighted U-value of each kind of surface in a room.

  U = Σ (Aᵢ × Uᵢ) ÷ Σ Aᵢ

  Energy model input file (IDF) and its results energy-ep.js

  • BimCraft
  64-bit

• Boundary of a surface

  Whether a surface of a room faces another room, the ground or the outside, and its corners as written.

  probe = mean of the corners + 0.6 m × outward normal

  Energy model input file (IDF) and its results energy-ep.js

  • BimCraft
  64-bit

• Window rectangle on its wall

  The four corners of a window as written on the wall it faces.

  k = √(area ÷ (span × height)); half width = span × k ÷ 2; half height = height × k ÷ 2; corners projected onto the wall plane

  Energy model input file (IDF) and its results energy-ep.js

  • BimCraft
  64-bit

• Glazing written for every window

  The one window construction every window in the file uses.

  U = 1.4 W/m²K, solar heat gain 0.6, visible transmittance 0.7

  Energy model input file (IDF) and its results energy-ep.js

  • BimCraft
  64-bit

• Site and time zone

  The latitude, longitude and time zone written to the file.

  time zone = round(longitude ÷ 15)

  Energy model input file (IDF) and its results energy-ep.js

  • BimCraft
  64-bit

• Design loads read back

  Each zone's design heating and cooling load in watts, from the engine's sizing report.

  Energy model input file (IDF) and its results energy-ep.js

  • BimCraft
  64-bit

• Yearly energy per zone

  Each zone's yearly heating and cooling energy in kilowatt-hours.

  kWh = J ÷ 3.6 × 10⁶

  Energy model input file (IDF) and its results energy-ep.js

  • BimCraft
  64-bit

• Difference between the two methods

  How far the engine's design loads are from the quick loads, per room.

  ratio = (engine − quick) ÷ quick

  Energy model input file (IDF) and its results energy-ep.js

  • BimCraft
  64-bit

• Rooms the two methods disagree on

  A note for each room whose design heating differs by more than 15 %.

  note when |ratio| > 0.15

  Energy model input file (IDF) and its results energy-ep.js

  • BimCraft
  64-bit

• A parameter's value as kept

  A typed or imported value made safe for its kind.

  Family geometry from parameters family-model.js

  • BimCraft
  64-bit

• When two sizes are the same

  The key that tells one size of a family from another.

  key = every input value rounded to 0.001

  Family geometry from parameters family-model.js

  • BimCraft
  64-bit

• Parameters driven by formulas

  The value of every parameter that has a formula.

  Family geometry from parameters family-model.js

  • BimCraft
  64-bit

• A solid's numbers

  The evaluated box, profile, depth, axis, angle, path and radius of each solid, and the check that it is not flat.

  box = (min, max) of each pair; a negative depth moves the start: at = at + depth, depth = −depth

  Family geometry from parameters family-model.js

  • BimCraft
  64-bit

• Copies in an array

  The solids of an array, each moved by a whole number of steps.

  copy i is moved by (dx × i, dy × i, dz × i), count = round(count expression)

  Family geometry from parameters family-model.js

  • BimCraft
  64-bit

• A family placed inside another

  The position and quarter-turn of a nested family.

  turns = rotation ÷ 90; accepted when round(turns × 10⁶) ÷ 10⁶ is a whole number; k = turns mod 4

  Family geometry from parameters family-model.js

  • BimCraft
  64-bit

• Quarter turn of a solid

  An evaluated solid turned 90° about the vertical axis.

  (x, y) → (−y, x)

  Family geometry from parameters family-model.js

  • BimCraft
  Exact

• Move a solid

  An evaluated solid moved by an offset in the family's axes.

  p → p + (dx, dy, dz), mapped to the profile plane's own axes

  Family geometry from parameters family-model.js

  • BimCraft
  64-bit

• Area of a profile

  The area of a profile with its arcs, used to refuse a flat outline.

  area = ½ Σ (xᵢ·yᵢ₊₁ − xᵢ₊₁·yᵢ) with arcs flattened to chords

  Family geometry from parameters family-model.js

  • BimCraft
  64-bit

• Is the profile on one side of the axis

  Whether a revolve's profile stays on one side of its axis.

  s = ((axis direction) × (p − axis start)) ÷ |axis|; sides counted beyond ±0.01 mm

  Family geometry from parameters family-model.js

  • BimCraft
  64-bit

• Middle point of a profile arc

  The point halfway along an arc given by its two ends and a bulge.

  sagitta = bulge × chord ÷ 2; middle = chord middle + sagitta × (dy, −dx) ÷ chord

  Family geometry from parameters family-model.js

  • BimCraft
  64-bit

• Chords of a profile arc

  The points inside an arc, for outlines that cannot hold a true arc.

  θ = 4·atan(bulge); n = max(2, ⌈|θ| ÷ 15°⌉); center = circle through start, middle and end

  Family geometry from parameters family-model.js

  • BimCraft
  64-bit

• Profile written to the file

  A closed profile as an IFC curve: lines and true arcs in IFC4, a polyline in IFC2X3.

  Family geometry from parameters family-model.js

  • BimCraft
  64-bit

• A solid written to the file

  One box, extrusion, revolve or swept solid as its IFC item.

  revolve axis direction = (u₁ − u₀, v₁ − v₀) ÷ L; angle = degrees × π ÷ 180 (file in radians)

  Family geometry from parameters family-model.js

  • BimCraft
  64-bit

• Plan outline written to the file

  The outline other programs see in plan: the family's symbol, or each solid's outline from above.

  Family geometry from parameters family-model.js

  • BimCraft
  64-bit

• Plan bounds of a solid

  The smallest plan rectangle round a solid.

  revolve: R = largest distance of a profile point from the axis; bounds = axis start ± R, joined with the profile

  Family geometry from parameters family-model.js

  • BimCraft
  64-bit

• A plan symbol's numbers

  The evaluated lines, rectangles, circles, arcs, outlines and texts of a family's 2D symbol.

  Family geometry from parameters family-symbol.js

  • BimCraft
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• Circles and arcs of a symbol

  A symbol's circle or arc as points.

  n = max(2, ⌈sweep ÷ 7.5°⌉); pᵢ = (cx + r·cos aᵢ, cy + r·sin aᵢ)

  Family geometry from parameters family-symbol.js

  • BimCraft
  64-bit

• A symbol placed in the plan

  The symbol turned by the element's rotation and moved to its place.

  (u, v) → (x + u·cos a − v·sin a, y + u·sin a + v·cos a), a = rotation × π ÷ 180

  Family geometry from parameters family-symbol.js

  • BimCraft
  64-bit

• Where a placed family stands

  A placed element's position and rotation in its level's plan.

  x = M₁₂, y = M₁₃, z = M₁₄; rotation = atan2(M₁, M₀) × 180 ÷ π

  Family geometry from parameters family-ops.js

  • BimCraft
  64-bit

• Connector written as a port

  A family's pipe or duct connector written on a placed element: its point, direction and nominal size.

  Family geometry from parameters family-ops.js

  • BimCraft
  64-bit

• Snap to a step

  A sketch coordinate moved to the nearest multiple of the grid step.

  v → round(v ÷ step) × step

  Family editor: sketch points, handles and solved sizes family-edit.js

  • BimCraft
  64-bit

• Quarter-arc bulge

  The bulge that makes a segment a quarter circle, and the cycle straight, left arc, right arc.

  bulge = tan(90° ÷ 4) = tan(π ÷ 8) = √2 − 1

  Family editor: sketch points, handles and solved sizes family-edit.js

  • BimCraft
  64-bit

• Move a sketch point

  A profile or path point moved to a new place.

  Family editor: sketch points, handles and solved sizes family-edit.js

  • BimCraft
  64-bit

• Set a segment's bulge

  Makes a profile segment straight or an arc of a given bulge.

  bulge = tan(angle ÷ 4), rounded to 12 decimals, |bulge| ≤ 10

  Family editor: sketch points, handles and solved sizes family-edit.js

  • BimCraft
  64-bit

• Bounds of a family

  The box round a family's visible solids.

  Family editor: sketch points, handles and solved sizes family-edit.js

  • BimCraft
  64-bit

• Height range of a solid

  The lowest and highest point of one solid.

  sweep: path z ± radius; revolve on the floor plane: at ± largest |profile point|

  Family editor: sketch points, handles and solved sizes family-edit.js

  • BimCraft
  64-bit

• Which parameter moves which face

  Finds, for each input length, the face of the family it pushes out.

  nudge the parameter by 10 mm; the face that moves most, and by more than 0.5 mm, is its handle

  Family editor: sketch points, handles and solved sizes family-edit.js

  • BimCraft
  64-bit

• Solve for a parameter

  The parameter value that puts a face or a hotspot at the dragged position.

  secant: c = b − f(b)·(b − a) ÷ (f(b) − f(a)); then bisection on a bracket; stop at |f| < 10⁻⁷

  Family editor: sketch points, handles and solved sizes family-edit.js

  • BimCraft
  64-bit

• Drag a hotspot

  The size values after a hotspot is dragged along its axis.

  x = solve(position(x) = dragged position); kept value = round(x × 1000) ÷ 1000

  Family editor: sketch points, handles and solved sizes family-edit.js

  • BimCraft
  64-bit