Calculations

Calculations

• Vented stream as CO2 equivalent

  The CO2-equivalent mass flow of a stream released to the air.

  CO2e = Σ F × zᵢ × MWᵢ × GWPᵢ

  Process emissions (CO2 equivalent) process/emissions.js

  • CadCraft
  • BimCraft
  64-bit

• Emissions report

  The emission of each tagged stream, fired unit and electric unit, the total per second and the total per year.

  fired: CO2e = |Q| ÷ efficiency ÷ 1.055056e9 × factor; electric: CO2e = (|W| + |Q|) ÷ 3.6e6 × grid factor; per year = total × 3600 × hours

  Process emissions (CO2 equivalent) process/emissions.js

  • CadCraft
  • BimCraft
  64-bit

• Number from a factor or cost cell

  A cell such as '$1,250.00' as a number.

  Imported carbon factors, prices and climate data data-packs.js

  • BimCraft
  64-bit

• Carbon factor from a file row

  A material's embodied-carbon factor in the unit the carbon pane works in.

  A1-A3 factor = value × unit factor (1 for kg, m, m², m³ and items; 0.001 for tonnes)

  Imported carbon factors, prices and climate data data-packs.js

  • BimCraft
  64-bit

• Monthly climate from NASA POWER

  Twelve monthly values of daily sunlight on a horizontal surface and of air temperature.

  ghi = value rounded to 0.01 kWh/m²/day; T = value rounded to 0.01 °C

  Imported carbon factors, prices and climate data data-packs.js

  • BimCraft
  64-bit

• Monthly climate from PVGIS

  Twelve monthly values of daily sunlight and air temperature, averaged over the years in the answer.

  ghi = Σ H(h)_m ÷ years ÷ days in month; T = Σ T2m ÷ years; both rounded to 0.01

  Imported carbon factors, prices and climate data data-packs.js

  • BimCraft
  64-bit

• Location sent to the climate provider

  The latitude and longitude put into the request address.

  latitude.toFixed(3), longitude.toFixed(3)

  Imported carbon factors, prices and climate data data-packs.js

  • BimCraft
  64-bit

• Is a ray to the sun blocked

  Whether the line from a point toward the sun meets a triangle of the model.

  det = e₁ · (d × e₂); u = (t · (d × e₂)) ÷ det; v = (d · (t × e₁)) ÷ det; hit if 0 ≤ u, 0 ≤ v, u + v ≤ 1 and distance > tMin

  Solar array shading pv-shade.js

  • BimCraft
  • CivilCraft
  64-bit

• Sample points on the modules

  The points on each module from which rays are cast.

  p = bilinear blend of the four corners at ((a + ½) ÷ k, (b + ½) ÷ k) + normal × lift

  Solar array shading pv-shade.js

  • BimCraft
  • CivilCraft
  64-bit

• Shade fraction by month and hour

  The share of the sample points in shadow at each of 12 × 24 sun positions.

  frac = shaded points ÷ points

  Solar array shading pv-shade.js

  • BimCraft
  • CivilCraft
  64-bit

• Beam light lost to shadows

  The share of the direct sunlight the array loses to shading, over the year or chosen months.

  loss = Σ beam × frac ÷ Σ beam

  Solar array shading pv-shade.js

  • BimCraft
  • CivilCraft
  64-bit

• Cell temperature

  The temperature of the cells from the air temperature and the light on the module.

  T_cell = T_amb + (NOCT − 20) ÷ 800 × G

  Solar yield estimate pv-yield.js

  • BimCraft
  • CivilCraft
  64-bit

• Module DC power

  The power of one module at a given irradiance and cell temperature.

  P = Wp × G ÷ 1000 × (1 + γ × (T_cell − 25))

  Solar yield estimate pv-yield.js

  • BimCraft
  • CivilCraft
  64-bit

• Loss chain

  The share of the DC energy left after soiling, mismatch, wiring, downtime and the inverter.

  chain = (1 − soiling) × (1 − mismatch) × (1 − wiring) × (1 − availability) × inverter efficiency

  Solar yield estimate pv-yield.js

  • BimCraft
  • CivilCraft
  64-bit

• Power in one hour

  The light on the array, the cell temperature and the DC and AC power for one hour of a month's representative day.

  G = beam × (1 − shade) + sky + ground; P = n × max(0, module power); AC before clipping = P ÷ 1000 × chain

  Solar yield estimate pv-yield.js

  • BimCraft
  • CivilCraft
  64-bit

• Monthly figures

  A month's light, shade loss and DC energy from its representative day.

  month = day × days in month; shade loss % = (unshaded − shaded) ÷ unshaded × 100

  Solar yield estimate pv-yield.js

  • BimCraft
  • CivilCraft
  64-bit

• Inverter clipping and monthly AC energy

  The AC energy of each month after the inverter's rating limits the hourly power.

  scale = P_ac ÷ Σ P when Σ P > P_ac; month AC = Σₕ P × scale × days, rounded to 0.1 kWh

  Solar yield estimate pv-yield.js

  • BimCraft
  • CivilCraft
  64-bit

• Annual energy, specific yield and performance ratio of an array

  An array's yearly DC and AC energy, kWh per kWp and performance ratio.

  AC = Σ rounded months; specific yield = AC ÷ kWp; PR = AC ÷ (kWp × POA)

  Solar yield estimate pv-yield.js

  • BimCraft
  • CivilCraft
  64-bit

• Plant totals

  The energy, specific yield, performance ratio, clipping and shade loss of all arrays together.

  PR = Σ AC ÷ Σ(kWp × POA); clipped % = clipped ÷ unclipped × 100

  Solar yield estimate pv-yield.js

  • BimCraft
  • CivilCraft
  64-bit

• Unit factor

  Chooses the factor that turns the file's unit into meters.

  k = meters per file unit, or 0.001 when that is missing, zero or not finite

  3DM import: units, placements and mesh points io/3dm-import.js

  • ModelCraft
  • PartCraft
  64-bit

• Mesh points in meters

  Scales a mesh's points and builds the model's mesh from them.

  p′ = p × k

  3DM import: units, placements and mesh points io/3dm-import.js

  • ModelCraft
  • PartCraft
  64-bit

• Block placement matrix

  Turns a block reference's matrix into the model's placement.

  m[c × 4 + r] = x[r × 4 + c]; translation × k

  3DM import: units, placements and mesh points io/3dm-import.js

  • ModelCraft
  • PartCraft
  64-bit

• Curve points in meters

  Scales each curve's points and drops segments of no length.

  a′ = a × k; kept when a′ ≠ b′

  3DM import: units, placements and mesh points io/3dm-import.js

  • ModelCraft
  • PartCraft
  64-bit

• Mesh record: 32-bit and 64-bit points

  Reads a mesh's points from the file and chooses between its 32-bit and 64-bit copies.

  use the 64-bit points when |aᵢ − vᵢ| ≤ |vᵢ| × 10⁻⁶ + 10⁻⁶ × max(1, |aᵢ|) for every coordinate

  3DM import: units, placements and mesh points io/3dm/objects.js

  • ModelCraft
  • PartCraft
  64-bit

• Single values by type

  Reads one property value with the width the file states.

  FBX reader: number types as stored io/fbx-parse.js

  • ModelCraft
  64-bit

• 64-bit whole numbers

  Reads a signed 64-bit whole number from two 32-bit halves.

  v = hi × 2³² + lo when −2²¹ ≤ hi < 2²¹; otherwise decimal text

  FBX reader: number types as stored io/fbx-parse.js

  • ModelCraft
  Exact

• Arrays by type

  Reads an array of floats, doubles or whole numbers.

  FBX reader: number types as stored io/fbx-parse.js

  • ModelCraft
  64-bit

• End derivative coefficients

  The factors that link the first control points to the first and second derivative at the start.

  a₁ = p ÷ (U[p+1] − U[1]); b₁ = p ÷ (U[p+2] − U[2]); c₂ = (p − 1) ÷ (U[p+1] − U[2])

  Matching and blending NURBS curves and surfaces nurbs/match.js

  • ModelCraft
  • PartCraft
  64-bit

• Point, direction and curvature at an end

  What a curve's end looks like to the curve that must meet it.

  t = C′ ÷ |C′|; out = ± t; speed = |C′|

  Matching and blending NURBS curves and surfaces nurbs/match.js

  • ModelCraft
  • PartCraft
  64-bit

• Curve end matched to a target

  Moves the first one to three control points so the curve meets the target with G0, G1 or G2.

  P₀ = T; P₁ = P₀ + out × speed ÷ a₁; D₂ = out (C″ · out) + κ speed²; P₂ = P₁ + (a₁ (P₁ − P₀) + D₂ ÷ c₂) ÷ b₁

  Matching and blending NURBS curves and surfaces nurbs/match.js

  • ModelCraft
  • PartCraft
  64-bit

• Blend curve between two ends

  A Bézier curve joining two curve ends with the asked continuity.

  G1: P₁ = A + out × α ÷ 3; G2: P₁ = A + out × α ÷ 5, P₂ = 2 P₁ − A + κ α² ÷ 20; α = chord × bulge

  Matching and blending NURBS curves and surfaces nurbs/match.js

  • ModelCraft
  • PartCraft
  64-bit

• Frame on the target's edge

  For a point near the target's edge: the nearest edge point, the outward direction in the tangent plane, the normal and the normal curvature.

  d = (n × tₑ) ÷ |n × tₑ|, turned to point away from the surface

  Matching and blending NURBS curves and surfaces nurbs/match.js

  • ModelCraft
  • PartCraft
  64-bit

• Surface edge matched to a target

  Refits the first one to three rows of control points so the surface meets the target along an edge.

  stations vᵢ = i ÷ M, M = max(samples, 4 × columns); rows fitted by least squares; accepted when gap ≤ g0, angle ≤ g1 and Δκ ≤ g2 (or relative ≤ g2rel)

  Matching and blending NURBS curves and surfaces nurbs/match.js

  • ModelCraft
  • PartCraft
  64-bit

• Blend surface between two edges

  A surface joining two surface edges, built from blend sections along them.

  sections at t = i ÷ n, n = 8, 16, … ≤ 128; each a Bézier of degree 1, 3 or 5; interpolated along the edge

  Matching and blending NURBS curves and surfaces nurbs/match.js

  • ModelCraft
  • PartCraft
  64-bit

• A number as STEP text

  Writes one real number into the file.

  String(x), with a decimal point added when it has none

  STEP files of NURBS curves and surfaces nurbs/step.js

  • ModelCraft
  • PartCraft
  64-bit

• Knots and multiplicities

  Turns a full knot vector into STEP's list of distinct knots with their counts.

  STEP files of NURBS curves and surfaces nurbs/step.js

  • ModelCraft
  • PartCraft
  64-bit

• Edges that have collapsed to a point

  Leaves a zero-length boundary edge, such as a pole, out of the face loop.

  skipped when arc length ≤ 10⁻⁹ × surface size

  STEP files of NURBS curves and surfaces nurbs/step.js

  • ModelCraft
  • PartCraft
  64-bit

• Trim loop written as a curve

  Writes a trim loop as one closed curve on the face.

  3D point = S(u, v) for each loop point; curve = straight segments through them

  STEP files of NURBS curves and surfaces nurbs/step.js

  • ModelCraft
  • PartCraft
  64-bit

• Length unit of a file

  Millimeters per file unit.

  SI: prefix × 1000; conversion-based: value × its base unit

  STEP files of NURBS curves and surfaces nurbs/step.js

  • ModelCraft
  • PartCraft
  64-bit

• Control points in millimeters

  Reads each control point and scales it by the file's unit.

  p′ = p × unit

  STEP files of NURBS curves and surfaces nurbs/step.js

  • ModelCraft
  • PartCraft
  64-bit

• Trim loops read back

  Turns a face's boundary edges into trim loops in the surface's own parameters.

  33 samples per curved edge; each projected to (u, v); outer when |area| < 0.999 × (u range × v range)

  STEP files of NURBS curves and surfaces nurbs/step.js

  • ModelCraft
  • PartCraft
  64-bit

• Quadrature nodes and weights

  The eight points and weights used to integrate the path's speed.

  Pattern along a path brep-bodies.js

  • PartCraft
  64-bit

• Length of the path

  The arc length of the path and the running length at each piece boundary.

  piece length = h Σ wᵢ |C′(m + h xᵢ)|, h = (b − a) ÷ 2, m = (a + b) ÷ 2; L = Σ pieces

  Pattern along a path brep-bodies.js

  • PartCraft
  64-bit

• Parameter at an arc length

  Finds the curve parameter that lies a given length along the path.

  tₙ₊₁ = tₙ − (s(tₙ) − s) ÷ |C′(tₙ)|, kept inside the bracket by bisection

  Pattern along a path brep-bodies.js

  • PartCraft
  64-bit

• Path point nearest the seed

  The arc length of the path point closest to the center of what is copied.

  root of (C(s) − p) · C′(s) = 0 by bisection, beside the nearest of 8 samples per piece

  Pattern along a path brep-bodies.js

  • PartCraft
  64-bit

• Turn of each copy

  Rotates each copy so it follows the path's direction without twisting.

  R ← rot(t_prev → t) × R, in n = ⌈distance ÷ (L ÷ 2000)⌉ steps between stations

  Pattern along a path brep-bodies.js

  • PartCraft
  64-bit

• Modal coordinate word

  Decides whether an address word such as X or Z is written on a line, and writes its value.

  written when round(v × 1000) ≠ round(last × 1000); text = letter + v to 3 decimals

  G-code written by text post definitions cam-postdef.js

  • PartCraft
  64-bit

• Numbers in a line template

  Fills the {variable} holes of a raw, comment or word template with values.

  G-code written by text post definitions cam-postdef.js

  • PartCraft
  64-bit

• Whole-number filter

  The int filter a post can put on a value, for example a spindle speed.

  int(s) = round(number(s))

  G-code written by text post definitions cam-postdef.js

  • PartCraft
  64-bit

• Arc center offsets I and J

  The center of an arc move, written relative to the start point.

  I = round₃(cₓ − round₃(X_last)); J = round₃(c_y − round₃(Y_last))

  G-code written by text post definitions cam-postdef.js

  • PartCraft
  64-bit