Calculations

Calculations

• Run to a steady state

  Steps the flow until it stops changing or a limit is reached.

  change = max |u′ − u| ÷ dt

  2D flow solver (finite volume) cfd/fv.js

  • CadCraft
  64-bit

• Velocity at cell centers

  The velocity at the center of each cell.

  u_c = ½(u_left + u_right); v_c = ½(v_bottom + v_top)

  2D flow solver (finite volume) cfd/fv.js

  • CadCraft
  64-bit

• Velocity at a point

  The velocity at any point of the region.

  2D flow solver (finite volume) cfd/fv.js

  • CadCraft
  64-bit

• Stream function

  The stream function at the cell corners.

  ψ(i, j) = ψ(i, j − 1) + U(i, j − 1) × h_y

  2D flow solver (finite volume) cfd/fv.js

  • CadCraft
  64-bit

• VTK export

  Writes velocity, pressure and tracer fields as a legacy ASCII VTK file.

  2D flow solver (finite volume) cfd/fv.js

  • CadCraft
  64-bit

• Mixing time

  The time at which a tracer's spread falls below a target.

  CV = √(Σ (c − mean)² ÷ n) ÷ mean

  2D flow solver (finite volume) cfd/fv.js

  • CadCraft
  64-bit

• Lattice directions and weights

  The nine directions of the lattice and the weight of each.

  w = 4/9, 1/9 (×4), 1/36 (×4)

  2D mixing solver (lattice Boltzmann) cfd/lbm.js

  • CadCraft
  64-bit

• Mixer set-up

  Creates the grid, the solid mask, the force field and the starting distributions.

  2D mixing solver (lattice Boltzmann) cfd/lbm.js

  • CadCraft
  64-bit

• Equilibrium distributions

  The equilibrium the flow and the tracer relax toward.

  f_eq = w ρ (1 + 3 c·u + 4.5 (c·u)² − 1.5 u²); g_eq = w C (1 + 3 c·u)

  2D mixing solver (lattice Boltzmann) cfd/lbm.js

  • CadCraft
  64-bit

• Collision step

  Density, velocity and tracer value of each cell, and the relaxation of its distributions.

  ρ = Σ f; u = (Σ f c + ½ F) ÷ ρ; f ← f − (f − f_eq) ÷ τ + source

  2D mixing solver (lattice Boltzmann) cfd/lbm.js

  • CadCraft
  64-bit

• Outlet condition

  Sets the last column of a flow-through box from its neighbor.

  f_out = f_eq(1, u_nb) + (f_nb − f_eq(ρ_nb, u_nb))

  2D mixing solver (lattice Boltzmann) cfd/lbm.js

  • CadCraft
  64-bit

• Velocity at a point

  The velocity reported at a position in the grid.

  2D mixing solver (lattice Boltzmann) cfd/lbm.js

  • CadCraft
  64-bit

• Result fields

  A copy of the velocity, speed, density or tracer field for reading or plotting.

  speed = √(u_x² + u_y²)

  2D mixing solver (lattice Boltzmann) cfd/lbm.js

  • CadCraft
  64-bit

• Mixing time

  The number of steps until the tracer is evenly spread.

  deviation = max |C − mean|; reached when deviation ≤ level × starting deviation

  2D mixing solver (lattice Boltzmann) cfd/lbm.js

  • CadCraft
  64-bit

• Residence time distribution

  The distribution of times a pulse of tracer takes to leave a flow-through box, with its mean, variance and the nominal time.

  E = flux ÷ Σ(flux × Δt); mean = Σ t E Δt; variance = Σ t² E Δt − mean²; nominal = V ÷ Q

  2D mixing solver (lattice Boltzmann) cfd/lbm.js

  • CadCraft
  64-bit

• VTK export

  Writes the velocity and tracer fields as a legacy ASCII VTK file.

  2D mixing solver (lattice Boltzmann) cfd/lbm.js

  • CadCraft
  64-bit

• Guard on every written measure

  Decides what is written when a value is missing or not a number.

  DWG object values written and read dwg/objects-write.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  64-bit

• Arc angles brought into one turn

  Brings an angle into the range from 0 up to 2π before it is written.

  r = a mod 2π; r + 2π when r < 0

  DWG object values written and read dwg/objects-write.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  64-bit

• Arc

  Writes an arc's center, radius and two angles.

  DWG object values written and read dwg/objects-write.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  64-bit

• Line

  Writes a line's two end points.

  DWG object values written and read dwg/objects-write.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  64-bit

• Polyline vertices

  Writes the vertices of a lightweight polyline.

  DWG object values written and read dwg/objects-write.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  64-bit

• Vertex widths

  Writes the start and end width at a polyline vertex.

  equal widths: one value, −|width|

  DWG object values written and read dwg/objects-write.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  64-bit

• Linetype pattern length

  The total length of a linetype's dash pattern.

  length = Σ |element length|

  DWG object values written and read dwg/objects-write.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  64-bit

• Text direction

  The x-axis direction written for a block of text.

  x axis = (cos θ, sin θ, 0)

  DWG object values written and read dwg/objects-write.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  64-bit

• Block scale

  Writes the three scale factors of a block reference in the format's compact form.

  DWG object values written and read dwg/objects-write.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  64-bit

• Single-line text

  Writes a text's insertion point, height, rotation, width factor and oblique angle.

  DWG object values written and read dwg/objects-write.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  64-bit

• Extension record values

  Writes the numbers kept in an extension record.

  DWG object values written and read dwg/objects-write.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  64-bit

• Block content matrix of a multileader

  The 4 × 4 matrix written for a multileader's block content when the model gives none.

  M = translate(l) · rotate_z(θ) · scale(s)

  DWG object values written and read dwg/mleader-write.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  64-bit

• Line read

  Reads a line's two end points.

  DWG object values written and read dwg/objects-read.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  64-bit

• Polyline vertices read

  Reads the vertices of a lightweight polyline.

  DWG object values written and read dwg/objects-read.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  64-bit

• North direction of older geolocation data

  Turns the north angle of a version 1 geolocation object into a direction vector.

  north = (sin a, cos a)

  DWG object values written and read dwg/objects-read.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  64-bit

• Fit point parameters and knots

  The parameter of each fit point along the spline, and the knot vector built from them.

  u₀ = 0; uᵢ = uᵢ₋₁ + |Qᵢ − Qᵢ₋₁|; knots = [0,0,0,0, u₁ … uₙ₋₂, L,L,L,L]

  Spline through fit points dwg/spline-fit.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  64-bit

• Cubic basis functions at a parameter

  The four B-spline basis values that weigh the control points at one fit point.

  Cox–de Boor recurrence, degree 3

  Spline through fit points dwg/spline-fit.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  64-bit

• Start condition

  The rows that pin the first control point and set the spline's start tangent or a natural start.

  P₀ = Q₀; P₁ − P₀ = T₀ × u₄ ÷ 3 or P₀ ÷ u₄ − P₁ (1 ÷ u₄ + 1 ÷ u₅) + P₂ ÷ u₅ = 0

  Spline through fit points dwg/spline-fit.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  64-bit

• End condition

  The rows that pin the last control point and set the spline's end tangent or a natural end.

  Pₘ₋₁ = Qₙ₋₁; Pₘ₋₁ − Pₘ₋₂ = T₁ × (L − uₘ₋₁) ÷ 3 or the zero second derivative row

  Spline through fit points dwg/spline-fit.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  64-bit

• Solve for the control points

  Solves the banded system for the x, y and z of every control point.

  A · P = B

  Spline through fit points dwg/spline-fit.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  64-bit

• Lineweight to the file's lineweight index

  Picks the stored lineweight that is nearest to the one the layer or object has.

  index = the i with the smallest |table[i] − lineweight|

  Values changed when a DWG is written dwg/write.js

  • CadCraft
  • ModelCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  Exact

• Ellipse with a ratio above 1

  Rewrites an ellipse whose minor axis is longer than its major axis so the file holds a ratio of 1 or less.

  major′ = (−m_y, m_x) × ratio; ratio′ = 1 ÷ ratio; start and end − π ÷ 2

  Values changed when a DWG is written dwg/write.js

  • CadCraft
  • ModelCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  64-bit

• Ray and construction line direction

  Writes the direction of a ray or construction line as a unit vector.

  d′ = d ÷ |d|

  Values changed when a DWG is written dwg/write.js

  • CadCraft
  • ModelCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  64-bit

• Drawing extents

  The lower left and upper right corner of model space written to the file header.

  min and max of x, y, z over the defining points

  Values changed when a DWG is written dwg/write.js

  • CadCraft
  • ModelCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  64-bit

• Default angles of a light

  The hotspot and falloff angles written for a light that has none of its own.

  hotspot = π ÷ 4; falloff = π ÷ 4 + 0.0872664626

  Values changed when a DWG is written dwg/solid-write.js

  • CadCraft
  • ModelCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  64-bit

• Standard gravity

  The acceleration that turns a member's or plate's mass into its own weight.

  g = 9.80665 m/s²

  Member axes and section properties frame/frame-model.js

  • CadCraft
  • BimCraft
  • DetailCraft
  Exact

• Member length and local axes

  The length of a member and the three unit vectors its forces and section are measured in.

  L = |P_j − P_i|; x = (P_j − P_i) ÷ L; z = unit(Z − (Z·x) x); y = z × x; then y and z turned by the roll

  Member axes and section properties frame/frame-model.js

  • CadCraft
  • BimCraft
  • DetailCraft
  64-bit

• Zero-length member test

  Removes a member whose two ends are at the same place.

  |P_j − P_i| < 1e-6 mm

  Member axes and section properties frame/frame-model.js

  • CadCraft
  • BimCraft
  • DetailCraft
  64-bit

• Area and second moments of a polygon section

  Area, centroid, second moments about the centroid, principal moments and their angle for a section outline with holes.

  A = ½ Σ cᵢ; Iyy = (1 ÷ 12) Σ (v₀² + v₀v₁ + v₁²) cᵢ − A c_v²; cᵢ = u₀v₁ − u₁v₀; I₁,₂ = (Iyy + Izz) ÷ 2 ± √(((Iyy − Izz) ÷ 2)² + Iyz²)

  Member axes and section properties frame/frame-model.js

  • CadCraft
  • BimCraft
  • DetailCraft
  64-bit

• Torsion constant

  The Saint-Venant torsion constant J of a catalog section or of an outline.

  I with fillets: J = ⅔ B T³ + ⅓ (D − 2T) t³ + 2 α D₁⁴ − 0.420 T⁴; open: Σ b t³ ÷ 3; tube: 4 Am² t ÷ p; round tube: π (D⁴ − (D − 2t)⁴) ÷ 32

  Member axes and section properties frame/frame-model.js

  • CadCraft
  • BimCraft
  • DetailCraft
  64-bit

• Section properties for the analysis

  Chooses the area, the two second moments, J and the roll a drawn section is analyzed with.

  A = the profile's exact area if given, else the polygon's; Iy, Iz = Iyy, Izz, or I₁, I₂ with roll = the principal angle

  Member axes and section properties frame/frame-model.js

  • CadCraft
  • BimCraft
  • DetailCraft
  64-bit

• A load split onto the member's axes

  Turns one point or distributed load in a global or local direction into pieces along the member's own three axes.

  piece = load × (direction · local axis); a, b clamped to [0, L]

  Frame analysis: loads, releases, end forces and reactions frame/frame-solve.js

  • CadCraft
  • BimCraft
  • DetailCraft
  64-bit

• Inverse of the released block

  Inverts the small stiffness block of a member's released end actions.

  Gauss–Jordan with partial pivoting

  Frame analysis: loads, releases, end forces and reactions frame/frame-solve.js

  • CadCraft
  • BimCraft
  • DetailCraft
  64-bit

• Member stiffness with released ends

  Removes pinned or sliding end actions from a member's 12 × 12 stiffness.

  k_c = k_kk − k_kr · k_rr⁻¹ · k_rk

  Frame analysis: loads, releases, end forces and reactions frame/frame-solve.js

  • CadCraft
  • BimCraft
  • DetailCraft
  64-bit