Calculations

Calculations

• Wire size

  The smallest wire whose ampacity, after derating, is at least the required current.

  smallest wire with ampacity × derate ≥ amps − 1e-9

  Solar one-line currents, devices and wires pv-oneline.js

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• A run on the diagram

  Records one run with its current, required current, device and wire.

  device and wire from the required current; stored current and required current rounded to 0.1 A

  Solar one-line currents, devices and wires pv-oneline.js

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• DC currents of an array

  The current of one string circuit and of the array's combined output, with the required values.

  per circuit = I_sc factor × continuous factor × I_sc; output = strings × I_sc; required = factor × output

  Solar one-line currents, devices and wires pv-oneline.js

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• Run from the DC disconnect to the inverter

  The current, device and wire of the run into each inverter.

  Solar one-line currents, devices and wires pv-oneline.js

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• AC current of an inverter

  The output current of one inverter at the service voltage.

  I = P_ac × 1000 ÷ (V × √3) for three-phase; I = P_ac × 1000 ÷ V for single-phase

  Solar one-line currents, devices and wires pv-oneline.js

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• Grid position from GeoTIFF tags

  The transform from cell column and row to map coordinates.

  x₀ = tie_X − tie_I × scale_X; y₀ = tie_Y + tie_J × scale_Y; pixel-is-point: x₀ −= ½(a + b), y₀ −= ½(d + e)

  Elevation grids read from GeoTIFF and ASCII files raster.js

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• Cell size

  The single cell size of a square, north-up grid.

  cell = a when b = d = 0 and |a + e| < 1e-9 × |a|

  Elevation grids read from GeoTIFF and ASCII files raster.js

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• ASCII grid header

  The size, cell size and lower-left corner of an ASCII grid.

  corner = center − cell ÷ 2 when the header gives cell centers

  Elevation grids read from GeoTIFF and ASCII files raster.js

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• ASCII grid position

  The transform of an ASCII grid, with its origin at the top-left corner.

  top = yll + rows × dy

  Elevation grids read from GeoTIFF and ASCII files raster.js

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• Elevation from a stored sample

  Turns one stored sample into an elevation, or into no value.

  z = v × scale + offset

  Elevation grids read from GeoTIFF and ASCII files raster.js

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• Reading a window of cells

  Reads part of the grid, optionally every step-th cell, into an array of elevations.

  columns = ceil((c₁ − c₀) ÷ step); rows = ceil((r₁ − r₀) ÷ step)

  Elevation grids read from GeoTIFF and ASCII files raster.js

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• Lowest and highest elevation

  The minimum and maximum elevation shown for a grid.

  Elevation grids read from GeoTIFF and ASCII files raster.js

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• Position of a georeferenced picture

  The transform and bounding box of a picture read at a reduced size.

  sₓ = width ÷ w, s_y = height ÷ h; affine = [x₀, a·sₓ, b·s_y, y₀, d·sₓ, e·s_y]

  Elevation grids read from GeoTIFF and ASCII files raster.js

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• Sun direction for a rendering

  The direction to the sun in the 3D view's axes.

  model = east × dₓ + north × d_y, with d_z kept; view = (mₓ, m_z, −m_y), normalized

  Rendering: sun direction, lamps and painted faces render-bim.js

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  32-bit, display only

• Lamps from light fixtures

  A lamp for each light fixture: where it is, how bright and how wide.

  lumens = stored value, else watts × 80, else 800; position = middle of the fixture's box, just under it

  Rendering: sun direction, lamps and painted faces render-bim.js

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• Which side of an element a face is

  Names the axis of the element's placement that a face normal runs along, to pick the material painted on that side.

  axis = the placement column with the largest |n · column|

  Rendering: sun direction, lamps and painted faces paint-bim.js

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  32-bit, display only

• Cabinet footprints in the plan

  Each counter-ready cabinet's footprint, as a rectangle or an L, in the level's plan.

  (X, Y) = (pₓ + x·cos r − y·sin r, p_y + x·sin r + y·cos r), then the level's inverse matrix

  Countertop outline and quantities res-counter.js

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• Countertop runs

  The outline, area and perimeter of each joined run of cabinets with the overhang added.

  front edge points += overhang × outward normal; run = union of the footprints

  Countertop outline and quantities res-counter.js

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• Point in a run

  Tests whether a point is inside a run's outline or on its edge.

  even-odd ray test, or within 1 mm of an edge

  Countertop outline and quantities res-counter.js

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• Countertop quantities

  The area, perimeter and front edge length stored for a countertop.

  Area = round(mm² ÷ 10⁶, 6) m²; FrontEdge = Σ lengths of the cabinets' front edges

  Countertop outline and quantities res-counter.js

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• Default dormer sizes

  The width, height, pitches, overhang and wall thickness a new dormer starts with.

  gable pitch = atan(8 ÷ 12) in degrees; shed pitch = atan(3 ÷ 12) in degrees; sizes = inches × 25.4

  Dormer geometry res-dormer.js

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• Dormer planes, walls and cut

  Every polygon of the dormer in 3D and the outline of the hole in the roof.

  t_v = T × √(1 + s_m²); shed: y_back = (H + t_vd) ÷ (s_m − s_d); gable: y_ridge = (H + s_d × w ÷ 2) ÷ s_m

  Dormer geometry res-dormer.js

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• A sloped polygon as a solid

  Sets up the frame and profile of a planar polygon swept straight up.

  n = unit((p₁ − p₀) × (p₂ − p₀)); x = unit(Z × n); y = n × x; sweep = (Z·x, Z·y, Z·n)

  Dormer geometry res-dormer.js

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• From the walls' level to the roof's level

  Moves the dormer's points and directions into the axes of the level that holds the roof.

  M = roof level⁻¹ × walls level; direction = M·v − M·0

  Dormer geometry res-dormer.js

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• Hole in the roof slab

  The outline and depth of the opening that the dormer cuts in its roof face.

  outline = M_slab · cut; depth = cutZ₁ − cutZ₀

  Dormer geometry res-dormer.js

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• Device spot on the nearest wall face

  The wall face nearest the pointer, the distance along it and the direction the device faces.

  s = clamp((p − a)·u, 0, L); distance to face = ||(p − a)·n| − t ÷ 2|; angle = atan2(side·n_y, side·nₓ)

  Electrical devices: positions, loads and circuit amps res-elec.js

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• Point on a wall face

  The plan point on a wall's face at a distance along the wall.

  at = a + s·u + side × (t ÷ 2)·n

  Electrical devices: positions, loads and circuit amps res-elec.js

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• Stored device position and body

  The device's placement, box and the X, Y and Angle kept for it.

  placement angle = angle × 180 ÷ π − 90; X, Y = round(mm ÷ unit, 6); Angle = round(degrees, 4)

  Electrical devices: positions, loads and circuit amps res-elec.js

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• Ceiling height of a level

  The height ceiling-mounted devices are placed at.

  middle value of the sorted wall heights; else max(2000, level height − 300)

  Electrical devices: positions, loads and circuit amps res-elec.js

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• Nominal voltage of a device

  The voltage used for a circuit's current, from the device kind and the unit system.

  metric: 230 V, three-phase socket 400 V; feet and inches: 120 V, cooker, heater, charger and three-phase socket 240 V

  Electrical devices: positions, loads and circuit amps res-elec.js

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• Circuit schedule

  The device count, load, current and voltage of each circuit.

  watts = Σ load; volts = highest nominal voltage on the circuit; amps = watts ÷ volts, to 1 decimal

  Electrical devices: positions, loads and circuit amps res-elec.js

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• Device schedule total

  The rows of the device schedule and the total load.

  total watts = round(Σ load)

  Electrical devices: positions, loads and circuit amps res-elec.js

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• Default footing size

  The footing's width and depth from the foundation kind, the number of stories and the wall material.

  width = table inches (+ 4 under masonry or concrete) × 25.4; depth = 10 in from 24 in wide, else 8 in

  Foundation parts and quantities res-foundation.js

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  Exact

• Outline offset inward

  A polygon moved inward by a distance, with mitred corners.

  corner = intersection of the two neighboring edges, each moved by d along its left normal

  Foundation parts and quantities res-foundation.js

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• Parts of a foundation

  The slab, edge beam, stem wall and footing outlines with their bottom and top heights.

  footing ring between offsets (t_stem − w_foot) ÷ 2 and (t_stem + w_foot) ÷ 2; footing top = −bottom + depth

  Foundation parts and quantities res-foundation.js

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• Footings stepped to the ground

  Splits each wall's footing and stem into runs whose underside steps down with the ground.

  underside = min(floor((ground − bottom) ÷ step) × step, −bottom), step = 8 × 25.4 mm; sampled every 600 mm

  Foundation parts and quantities res-foundation.js

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• Cutting a strip between two cross lines

  Keeps the part of a wall's strip between two distances along the wall.

  t = f_a ÷ (f_a − f_b); point = a + t × (b − a)

  Foundation parts and quantities res-foundation.js

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• Ground height under the foundation

  The ground's height relative to the floor at a plan point.

  world = M · (x, y); height = ground(world) − level elevation

  Foundation parts and quantities res-foundation.js

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• Quantities of a ring or slab

  Area, length, width, height and volume of a slab, stem wall or footing.

  a = |A_outer| − |A_inner|; length = (P_outer + P_inner) ÷ 2; width = a ÷ length; volume = a × h

  Foundation parts and quantities res-foundation.js

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• Quantities of a stepped footing or stem

  The length and volume of a footing or stem wall made of stepped pieces.

  volume = Σ |A_piece| × height; length = Σ P_piece ÷ 2

  Foundation parts and quantities res-foundation.js

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• Lumber size for a span

  Picks the smallest size in a span table whose maximum span reaches the span, or the largest size flagged as over.

  first size with span ≤ max + 1e-6 mm

  Wall, floor and roof framing layout res-framing.js

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• Span table column for a spacing

  Chooses the 16 inch or the 24 inch column of a span table from the framing spacing.

  |spacing − 609.6| < 50 → 24 inch column, else 16 inch column

  Wall, floor and roof framing layout res-framing.js

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• Header size for an opening

  Picks a two-ply header size from the rough opening width, or three plies of 2x12 flagged as over.

  first size with width ≤ max + 1e-6 mm; non-bearing: 2x4 up to 8 ft

  Wall, floor and roof framing layout res-framing.js

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• Board feet of a piece

  The board feet of one piece from its nominal size and its length.

  bf = t_nominal × d_nominal × (L ÷ 304.8) ÷ 12

  Wall, floor and roof framing layout res-framing.js

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• Stud layer position across a wall

  Finds where the stud layer sits across the wall's thickness, from the wall type's layers.

  y = ±(t ÷ 2 − Σ layers before − layer thickness)

  Wall, floor and roof framing layout res-framing.js

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• Where a wall's framing starts and stops

  Finds the framed start and end of a wall at corners and T junctions with other walls.

  t = cross(q − p, e) ÷ cross(d, e)

  Wall, floor and roof framing layout res-framing.js

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• Length of a wall piece

  Records a wall piece as a box and takes its length as the longer of its extent along the wall and its height.

  length = max(x₁ − x₀, z₁ − z₀)

  Wall, floor and roof framing layout res-framing.js

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• Framing around a wall opening

  Places the jack and king studs, the header, the cripples and the rough sill around each door and window.

  header top = min(head + header depth, underside of top plate); cripples at x₀ + k × spacing

  Wall, floor and roof framing layout res-framing.js

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• Studs on layout

  Places the common studs on center from the wall's framed start.

  x = x₀ + k × spacing, k = 1, 2, … while x < x₁ − T

  Wall, floor and roof framing layout res-framing.js

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• Line clipped to a polygon

  Finds the stretches of a joist, rafter or truss line that lie inside a floor outline or a roof face.

  t = cross(a − p, e) ÷ cross(d, e); s = cross(a − p, d) ÷ cross(d, e)

  Wall, floor and roof framing layout res-framing.js

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