Calculations

Calculations

• Leg dimension

  The dimension line beside each leg and the number on it.

  real = √(Δx² + Δy² + Δz²) of the leg's 3D ends

  Piping isometric drawing and its bill of materials addons/plant/lib/iso.js

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• Coordinates in the DXF file

  Formats paper coordinates, text heights and text angles for the DXF output.

  num(v) = v rounded to 4 decimals

  Piping isometric drawing and its bill of materials addons/plant/lib/iso.js

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• Coordinates in the SVG file

  Formats paper coordinates for the SVG output and flips Y to run downward.

  f(n) = n to 2 decimals; Y = paper height − y

  Piping isometric drawing and its bill of materials addons/plant/lib/iso.js

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• Corners of an item

  The four corners in plan of an item of given width, depth, position and turn.

  corner = (x₀ + x cos a − y sin a, y₀ + x sin a + y cos a), a = rot × π ÷ 180

  Factory layout checks addons/plant/lib/layout.js

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• Access strips

  The strips beside each side of an item that must stay free, as turned rectangles.

  Factory layout checks addons/plant/lib/layout.js

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• Overlap of two convex polygons

  Whether two items, or an item and an access strip or obstacle, overlap by more than a sliver.

  separated if maxA ≤ minB + tol or maxB ≤ minA + tol on any edge normal; tol = 1

  Factory layout checks addons/plant/lib/layout.js

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• Distance from a point to a segment

  The shortest distance from a corner of one item to an edge of another.

  t = clamp(((p − a) · (b − a)) ÷ |b − a|², 0, 1); d = |p − (a + t (b − a))|

  Factory layout checks addons/plant/lib/layout.js

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• Gap between two items

  The least distance between two items that do not overlap, compared with the minimum aisle width.

  gap = min over corners and edges of the point-to-segment distance

  Factory layout checks addons/plant/lib/layout.js

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• Floor load of an item

  The weight of an item divided by its footprint area, compared with the floor load limit.

  load = weight ÷ (area ÷ 10⁶) in kg per m²; area = |Σ (xᵢ yᵢ₊₁ − xᵢ₊₁ yᵢ)| ÷ 2

  Factory layout checks addons/plant/lib/layout.js

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• Footprint of Plant equipment

  The width, depth, height and center of a piece of Plant equipment for the layout, from its bounding box.

  Factory layout checks addons/plant/lib/layout.js

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• Flow path length

  The length of the path through a sequence of items, measured center to center along X then Y.

  L = Σ (|Δx| + |Δy|)

  Factory layout checks addons/plant/lib/layout.js

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• Legs of a route

  The straight legs of a route with their axis and length.

  axis = first of x, y, z with |Δ| > 10⁻⁶; length = |Δ| on that axis

  Orthogonal pipe router addons/plant/lib/route.js

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• Route against obstacles

  Whether the center line of a route comes within a clearance of any obstacle box.

  Orthogonal pipe router addons/plant/lib/route.js

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• Grid lines of the search

  The X, Y and Z coordinates at which a route may turn.

  lines = nozzle and lead coordinates, obstacle faces ± clearance, levels, two outer lines, and the midpoint of each neighboring pair

  Orthogonal pipe router addons/plant/lib/route.js

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• Search state and the minimum leg

  The key that identifies a search state: grid node, direction and the length of the current leg.

  cap = round(minLeg); key = ((node × 6 + direction) × (cap + 1)) + min(cap, round(run))

  Orthogonal pipe router addons/plant/lib/route.js

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• Cost of a step

  The cost added for moving to the next grid node.

  cost = g + step × (1 + climbCost if vertical, else 1) + (bendCost if the direction changes)

  Orthogonal pipe router addons/plant/lib/route.js

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• Route points and length

  The final corner points of the route with collinear points removed, its length, bends and climbs.

  length = Σ leg lengths; bends = legs − 1

  Orthogonal pipe router addons/plant/lib/route.js

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• Openings and walls on a room's edge

  Finds the doors, windows and walls that lie on the outline of a room.

  t = clamp(((p − a) · (b − a)) ÷ |b − a|², 0, 1); d = |p − a − t (b − a)|; on the edge if d ≤ tolerance

  Rooms handed to add-ons with their doors, windows and walls addons/bimcraft-api.js

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• Openable share of a window

  How much of a window opens, from its type name.

  fixed, picture, transom: 0; hung: 0.5; anything else: 1

  Regulation checks of rooms, doors, windows and outlets addons/regs/lib/check.js

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• Net clear opening of a window

  The clear width, height and area of a window for the escape opening rules, estimated from its type.

  hung: w × h ÷ 2; slider: w ÷ 2 × h; other opening types: w × h; fixed: 0

  Regulation checks of rooms, doors, windows and outlets addons/regs/lib/check.js

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• Least width of a room

  The narrowest width across a room outline, used for the least room dimension and hall width rules.

  min over edges of (max − min of p · n), n = unit normal of the edge

  Regulation checks of rooms, doors, windows and outlets addons/regs/lib/check.js

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• Window area credited to a room

  Adds each window's area and openable area to the room on either face of its wall.

  center = a + u × (offset + width ÷ 2); area = width × height; open = area × share

  Regulation checks of rooms, doors, windows and outlets addons/regs/lib/check.js

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• Ceiling height, light and ventilation of a room

  The values compared with the ceiling height, natural light and ventilation rules.

  ceiling = lowest wall height on the level; light % = window area ÷ floor area × 100; vent % = openable area ÷ floor area × 100

  Regulation checks of rooms, doors, windows and outlets addons/regs/lib/check.js

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• Egress door clear width

  Finds the widest exterior door and its clear width and height for the egress door rules.

  clear width = max(0, leaf width − 50.8)

  Regulation checks of rooms, doors, windows and outlets addons/regs/lib/check.js

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• Position of a point along a room's perimeter

  The distance along the room outline to the point nearest an outlet or a door, and the outline's total length.

  s = Σ earlier edge lengths + t × L; t = clamp(((p − a) · (b − a)) ÷ L², 0, 1)

  Regulation checks of rooms, doors, windows and outlets addons/regs/lib/check.js

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• Longest distance to an outlet along the wall

  The greatest distance, measured along the floor line, from any point of a wall space to an outlet in that space.

  per wall space: max(first, length − last, half of each gap between neighbors); a space with no doorway: (first + length − last) ÷ 2

  Regulation checks of rooms, doors, windows and outlets addons/regs/lib/check.js

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• Numbers in the regulation schedule

  Formats a found value or a limit for the schedule table.

  percent: 1 decimal; m²: 2 decimals; ratio and U-value: 2 decimals; R-value: 1 decimal; count: whole number

  Regulation checks of rooms, doors, windows and outlets addons/regs/lib/check.js

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• Rooms and doors of the escape routes

  Builds the graph of rooms and the doors that join them or lead outside, with each door's clear width.

  clear width = max(0, leaf width − 50.8)

  Regulation checks of rooms, doors, windows and outlets addons/regs/lib/route.js

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• Narrowest door on the way out of a room

  The finding for each room: the narrowest door on its best way out against the pack's egress width.

  utilization = minimum ÷ bottleneck; stated width = round(bottleneck)

  Regulation checks of rooms, doors, windows and outlets addons/regs/lib/route.js

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• Footing width and thickness from the table

  The footing size the pack's table gives for the number of stories, the foundation type, the snow load and the soil pressure.

  width = inches × 25.4; thickness = inches × 25.4

  Regulation limits read from the pack's tables addons/regs/lib/check.js

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• Footing depth below grade

  The depth of the footing's underside below grade compared with the rule and the frost depth.

  required = max(rule, frost depth); found = max(0, depth below the floor − 6 × 25.4)

  Regulation limits read from the pack's tables addons/regs/lib/check.js

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• Feet and inches in a table cell

  Turns a span written as feet-inches in a table into millimeters.

  mm = (feet × 12 + inches) × 25.4

  Regulation limits read from the pack's tables addons/regs/lib/check.js

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• Header span from the table

  The allowed span of a header for its size, what it carries, the snow load and the building width.

  span = a + (b − a) × (w − lo) ÷ (hi − lo), w = building width ÷ 304.8

  Regulation limits read from the pack's tables addons/regs/lib/check.js

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• Span of a header in the model

  The span of a framed header compared with the table.

  span = max(0, length − 3 × 25.4)

  Regulation limits read from the pack's tables addons/regs/lib/check.js

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• Stud height and spacing from the table

  The greatest stud height and spacing the table allows for a stud size, bearing or not, and the floors above.

  height = feet × 304.8; spacing = inches × 25.4

  Regulation limits read from the pack's tables addons/regs/lib/check.js

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• Joist and rafter span from the table

  The allowed span of a joist or rafter size at its spacing.

  column = first listed spacing ≥ spacing ÷ 25.4 − 0.05; span = least span of the listed species

  Regulation limits read from the pack's tables addons/regs/lib/check.js

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• Horizontal span of a rafter

  The span of the longest rafter or ceiling joist measured on the horizontal, compared with the table.

  span = sloped length × cos(pitch × π ÷ 180)

  Regulation limits read from the pack's tables addons/regs/lib/check.js

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• Insulation R-value of a wall type

  The nominal R-value of a wall type's cavity and continuous insulation layers, in imperial units.

  R = thickness (mm) ÷ 1000 ÷ λ × 5.678263

  Regulation limits read from the pack's tables addons/regs/lib/check.js

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• Wall insulation against the table's options

  Whether a wall type's insulation meets any of the cavity and continuous options of its climate zone.

  met if cavity + 0.05 ≥ option cavity and continuous + 0.05 ≥ option continuous, for any option

  Regulation limits read from the pack's tables addons/regs/lib/check.js

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• K-factor in SI units

  Converts a head's K-factor from L/min per √bar to m³/s per √Pa.

  k = K ÷ 1000 ÷ 60 ÷ √100000

  Sprinkler layout and hydraulic calculation addons/sprinkler/lib/hydraulics.js

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• Pipe friction

  The friction loss in pascals per meter of pipe for a flow, an inside diameter and a roughness coefficient C.

  Δp per m = 10.67 × Q^1.852 ÷ (C^1.852 × D^4.871) × 998.2 × 9.80665

  Sprinkler layout and hydraulic calculation addons/sprinkler/lib/hydraulics.js

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• Pipe sizes

  Chooses for each pipe the smallest steel schedule 40 size that keeps the velocity within the limit.

  Q = heads below × flow per head ÷ 1000 × 1.15; v = Q ÷ (π d² ÷ 4) ≤ vmax

  Sprinkler layout and hydraulic calculation addons/sprinkler/lib/hydraulics.js

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• Design areas to test

  The groups of heads tried as the design area: blocks of rows at the far and near ends of the branch lines.

  heads = ceil(area ÷ coverage); per row m = ceil(1.2 × √area ÷ spacing); rows = ceil(heads ÷ m)

  Sprinkler layout and hydraulic calculation addons/sprinkler/lib/hydraulics.js

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• Minimum flow and pressure at a head

  The least flow and pressure every operating head must have.

  q = density ÷ 1000 ÷ 60 × coverage; P = max((q ÷ k)², minimum head pressure)

  Sprinkler layout and hydraulic calculation addons/sprinkler/lib/hydraulics.js

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• Pressures and flows for a source pressure

  The pressure at every node and the flow in every pipe when the source is at a given pressure and each operating head discharges K √P.

  P(b) = P(a) − friction × (length + equivalent length) − ρ g Δz

  Sprinkler layout and hydraulic calculation addons/sprinkler/lib/hydraulics.js

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• Lowest source pressure

  The lowest source pressure at which every operating head has its minimum.

  upper bound doubled from 200000 Pa until it works, then halved 40 times

  Sprinkler layout and hydraulic calculation addons/sprinkler/lib/hydraulics.js

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• Head and pipe results

  Each head's flow, pressure and density, each pipe's flow, velocity and pressure drop, and the total flow.

  density = q × 1000 × 60 ÷ coverage; v = Q ÷ (π D² ÷ 4); total = Σ head flows

  Sprinkler layout and hydraulic calculation addons/sprinkler/lib/hydraulics.js

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• Supply pressure at a flow

  The pressure the water supply gives at a flow, from the static and residual pressures of a flow test.

  P = Ps − (Ps − Pr) × (Q ÷ Qr)^1.85

  Sprinkler layout and hydraulic calculation addons/sprinkler/lib/hydraulics.js

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• Required against available pressure

  Takes the design area needing the most pressure, adds the hose allowance and margin, and compares with the supply.

  Q total = Q heads × 60 + hose; required = P source ÷ 100000 + margin; ok if available ≥ required − 10⁻⁹

  Sprinkler layout and hydraulic calculation addons/sprinkler/lib/hydraulics.js

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• Head spacing

  The number of heads each way and their spacing, the largest the hazard's maximum spacing and coverage allow.

  nx = ceil(W ÷ maxS − 10⁻⁹); ny likewise; raised until (W ÷ nx)(D ÷ ny) ≤ max coverage; sx = W ÷ nx

  Sprinkler layout and hydraulic calculation addons/sprinkler/lib/layout.js

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