Calculations

Calculations

• Lead time in days

  Reads a lead time such as 2-3 weeks or 5 business days as a number of days.

  weeks × 7; months × 30; business days → ⌈n × 7 ÷ 5⌉; result rounded to 0.1 day

  Supplier stock and lead-time check lib-supply/supply.js

  • TakeoffCraft
  • DetailCraft
  64-bit

• Price from text

  Reads a price cell as a whole number of 1/10000 dollar.

  price = round(n × 10000)

  Supplier stock and lead-time check lib-supply/supply.js

  • TakeoffCraft
  • DetailCraft
  64-bit

• A need in the supplier's unit

  The needed quantity in the unit the supplier's row uses.

  tonnes = kilograms ÷ 1000

  Supplier stock and lead-time check lib-supply/supply.js

  • TakeoffCraft
  • DetailCraft
  64-bit

• Short, late or in stock

  For each need: the matching supplier row, the shortfall and the status.

  short = max(0, need − stock); late: no stock figure and lead > limit

  Supplier stock and lead-time check lib-supply/supply.js

  • TakeoffCraft
  • DetailCraft
  64-bit

• Values in the reported problems

  The required and found values of a shortage or a long lead time in the problems list.

  Supplier stock and lead-time check lib-supply/supply.js

  • TakeoffCraft
  • DetailCraft
  64-bit

• Stock figure from text

  Reads a stock cell such as 1,200 or Out of stock as a number, or as in stock or not.

  Supplier stock and lead-time check supply.js

  • TakeoffCraft
  • DetailCraft
  64-bit

• Lead time in days

  Reads a lead time such as 2-3 weeks or 5 business days as a number of days.

  weeks × 7; months × 30; business days → ⌈n × 7 ÷ 5⌉; result rounded to 0.1 day

  Supplier stock and lead-time check supply.js

  • TakeoffCraft
  • DetailCraft
  64-bit

• Price from text

  Reads a price cell as a whole number of 1/10000 dollar, the unit the takeoff's rates use.

  price = round(n × 10000)

  Supplier stock and lead-time check supply.js

  • TakeoffCraft
  • DetailCraft
  64-bit

• Short, late or in stock

  For each estimate row with a quantity: the matching supplier row, the shortfall and the status.

  short = max(0, need − stock); late: no stock figure and lead > limit

  Supplier stock and lead-time check supply.js

  • TakeoffCraft
  • DetailCraft
  64-bit

• Values in the reported problems

  The required and found values of a shortage or a long lead time in the problems list.

  Supplier stock and lead-time check supply.js

  • TakeoffCraft
  • DetailCraft
  64-bit

• Supplier prices into the price library

  Sets a library entry's material rate to the matching supplier row's price.

  Supplier stock and lead-time check supply.js

  • TakeoffCraft
  • DetailCraft
  64-bit

• Cost of one call

  The cost of a call from its token counts and the model's prices.

  cost = (in × price in + out × price out) ÷ 1,000,000

  Spending on a person's own AI model ai-byok.js Every app
  64-bit

• Spending today and this month

  The cost, tokens and number of calls for the current day and month, and the calls in the last hour.

  amount = Σ cost of the calls in the period

  Spending on a person's own AI model ai-byok.js Every app
  64-bit

• Check before a call

  Refuses a call when the calls per hour, the day's or month's spending, or the day's tokens could pass a limit.

  refuse when spent + worst-case cost > limit; worst case = cost(estimated input, largest allowed output)

  Spending on a person's own AI model ai-byok.js Every app
  64-bit

• Recorded cost and the token estimate

  Stores each call's cost and estimates the input tokens of the next request.

  estimated tokens = ⌈JSON length ÷ 3⌉ + 500

  Spending on a person's own AI model ai-byok.js Every app
  64-bit

• Flow through a passage

  Persons per second through a door or corridor of a given width.

  rate = max(0, Fsm × (width − 2 × boundary))

  People flow and evacuation time people.js Every app
  64-bit

• Speed and specific flow at a density

  Walking speed and flow per meter of width at a given density of people.

  S = k × (1 − 0.266 × D); Fs = S × D; k = 1.4 m/s

  People flow and evacuation time people.js Every app
  64-bit

• Rate and speed of each passage

  The flow rate and walking speed each passage gets, from its own values or the defaults for its kind.

  People flow and evacuation time people.js Every app
  64-bit

• Door service time and walking time

  How long a door takes per person, how long the passage takes to walk, and each room's distance to an exit in time.

  service = 1 ÷ rate; walk = length ÷ speed; to exit = least total walking time

  People flow and evacuation time people.js Every app
  64-bit

• Which way a room empties

  The next passage for people in a room: the one with the least remaining walking time to an exit.

  keep a hop when toExit(next) < toExit(room) − 1e-9; choose the least walk + toExit(next)

  People flow and evacuation time people.js Every app
  64-bit

• Evacuation results

  People evacuated, the time the last person reaches an exit, peak occupancy and density per room, and queues per door.

  time = latest arrival at any exit; density = peak people in a room ÷ its area

  People flow and evacuation time people.js Every app
  64-bit

• Joint frames at a pose

  Each joint's rotation and offset from its parent at the given joint values.

  Rigid-body dynamics of a mechanism dynamics.js Every app
  64-bit

• Joint torques for a motion (inverse dynamics)

  The torque or force each joint needs for given positions, velocities and accelerations, with gravity, external loads and damping.

  outward: ω, α, a of each link; F = m × a_com; N = I α + ω × (I ω); inward: τᵢ = axis · n (revolute) or axis · f (prismatic) + damping × q̇ᵢ

  Rigid-body dynamics of a mechanism dynamics.js Every app
  64-bit

• Mass matrix

  The joint-space mass matrix at a pose.

  column j = rnea(q, q̇ = 0, q̈ = unit vector j) with no gravity, damping or external loads

  Rigid-body dynamics of a mechanism dynamics.js Every app
  64-bit

• Joint accelerations for given torques (forward dynamics)

  The acceleration of each joint under applied torques.

  M q̈ = τ − h

  Rigid-body dynamics of a mechanism dynamics.js Every app
  64-bit

• Kinetic and potential energy

  The mechanism's kinetic, potential and total energy at a pose and velocity.

  KE = ½ q̇ᵀ M q̇; PE = −Σ m × (g · p_com)

  Rigid-body dynamics of a mechanism dynamics.js Every app
  64-bit

• Simulated motion over time

  Joint positions and velocities at each time step under gravity and applied torques.

  RK4: y₊ = y + dt ÷ 6 × (k₁ + 2k₂ + 2k₃ + k₄); steps = round(T ÷ dt); t = step × dt

  Rigid-body dynamics of a mechanism dynamics.js Every app
  64-bit

• Courtyard of a footprint

  The rectangle around all pads, grown by a margin.

  courtyard = (min(x − w ÷ 2) − m, min(y − h ÷ 2) − m, max(x + w ÷ 2) + m, max(y + h ÷ 2) + m)

  Parametric PCB footprints footlib.js Every app
  64-bit

• Two-terminal chip

  Two pads at half the pitch either side of the center.

  x = ∓ pitch ÷ 2

  Parametric PCB footprints footlib.js Every app
  64-bit

• Dual-row surface-mount package

  Pads in two rows, numbered counter-clockwise from the top left.

  y = ((n ÷ 2 − 1) ÷ 2 − i) × pitch; x = ∓ row spacing ÷ 2

  Parametric PCB footprints footlib.js Every app
  64-bit

• Dual in-line through-hole package

  Drilled pads in two rows.

  y = ((n ÷ 2 − 1) ÷ 2 − i) × pitch; x = ∓ row spacing ÷ 2

  Parametric PCB footprints footlib.js Every app
  64-bit

• Pin header

  Drilled pads in one or two rows at a pitch.

  x = (r − (rows − 1) ÷ 2) × pitch; y = ((n − 1) ÷ 2 − i) × pitch

  Parametric PCB footprints footlib.js Every app
  64-bit

• Quad flat package

  Pads on four sides, numbered counter-clockwise from the top left.

  along a side: ((n − 1) ÷ 2 − i) × pitch; across: ± span ÷ 2

  Parametric PCB footprints footlib.js Every app
  64-bit

• Axial through-hole part

  Two drilled pads at half the lead pitch either side of the center.

  x = ∓ pitch ÷ 2

  Parametric PCB footprints footlib.js Every app
  64-bit

• Span text to millimeters

  A listed span, as a number or as feet-inches text, in millimeters.

  mm = ft × 304.8 + (in + n ÷ d) × 25.4

  Joist depth from a span table the person loads tji-table.js

  • BimCraft
  64-bit

• Table units to millimeters

  Depth, spacing and bearing of the loaded table in millimeters.

  Joist depth from a span table the person loads tji-table.js

  • BimCraft
  64-bit

• Spacing match

  Whether a requested on-center spacing is served by a listed column.

  0.98 × listed ≤ want ≤ 1.005 × listed

  Joist depth from a span table the person loads tji-table.js

  • BimCraft
  64-bit

• Smallest depth that reaches the span

  The joist size for a span, spacing and load case.

  first candidate with max + 10⁻⁶ ≥ span

  Joist depth from a span table the person loads tji-table.js

  • BimCraft
  64-bit

• Listed maximum span for a size

  The listed span of a named framing size at a spacing and case.

  Joist depth from a span table the person loads tji-table.js

  • BimCraft
  64-bit

• Depth written on the drawing

  The depth text used in the size label.

  in = round(mm ÷ 25.4 × 1000) ÷ 1000

  Joist depth from a span table the person loads tji-table.js

  • BimCraft
  64-bit

• Summed K of a list of fittings

  The total loss coefficient of the fittings on one link at its own Reynolds number and diameter.

  K = Σ nᵢ × Kᵢ(Re, D)

  Fitting losses summed from a pack process/equip/fittingk.js

  • CadCraft
  • BimCraft
  64-bit

• Head loss of a fitting

  The head loss in meters from K and the velocity.

  h = K × v² ÷ (2g)

  Fitting losses summed from a pack process/equip/fittingk.js

  • CadCraft
  • BimCraft
  64-bit

• Meets the limit

  True, false or null for a found value against a rule.

  min − e ≤ found ≤ max + e

  Pass or fail against a regulation limit addons/regs/lib/rows.js

  • CadCraft
  • BimCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Material and band thicknesses

  The thickness of each library sheet and edge band in millimeters and in inches.

  Cabinet material sizes, grooves and drill files addons/cabinetcraft/lib/materials.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  Exact

• Rules from the material picks

  The thicknesses, groove and band thicknesses that the construction rules use.

  groove = min(tback, 0.6 × tcarcass)

  Cabinet material sizes, grooves and drill files addons/cabinetcraft/lib/materials.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Sheet size for a material

  The sheet width and height a material is cut from.

  in = round(mm ÷ 25.4 × 4) ÷ 4

  Cabinet material sizes, grooves and drill files addons/cabinetcraft/lib/materials.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Hole positions in the drill XML

  The x and y of each hole as written in the drill file.

  x = round(x × 1000) ÷ 1000

  Cabinet material sizes, grooves and drill files addons/cabinetcraft/lib/export.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• G-code scale and thickness

  The unit scale and cut depth passed to the sheet G-code writer.

  thickness_mm = thickness × scale

  Cabinet material sizes, grooves and drill files addons/cabinetcraft/lib/export.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Run point to viewer frame

  A run point in the viewer frame in meters.

  p = Lm · C · (storey · p ÷ 1000)

  MEP openings and clearances shown and exported mep/structure-ui.js

  • BimCraft
  64-bit

• Opening rows in the CSV

  The insulation, size, X, Y, Z and through length of an opening as written in the CSV.

  v = round(mm)

  MEP openings and clearances shown and exported mep/structure-ui.js

  • BimCraft
  64-bit