Calculations

Calculations

• Row spacing without winter shade

  The distance between ground rows that leaves no shade at the winter solstice.

  h = slant × sin β; shadow = h ÷ tan α × max(0, cos Δaz); pitch = slant × cos β + shadow

  Solar array layout on roofs and ground pv.js

  • BimCraft
  • CivilCraft
  64-bit

• Ground rows of tables

  The tables and modules of a ground array with their corners, the pitch and the ground cover ratio.

  table width = n × across + (n − 1) × gap; row origin = origin − facing × pitch × r; GCR = slant ÷ pitch

  Solar array layout on roofs and ground pv.js

  • BimCraft
  • CivilCraft
  64-bit

• Compass frame of the site

  The north and east unit vectors in the model's plan.

  north = n ÷ |n|; east = (north_y, −northₓ)

  Sun position and light on a tilted plane for solar pv-sun.js

  • BimCraft
  • CivilCraft
  64-bit

• Clock hour for a solar hour

  The clock time at which the sun's time is a given hour.

  clock = solar − (equation of time + 4 × longitude − 60 × time zone) ÷ 60

  Sun position and light on a tilted plane for solar pv-sun.js

  • BimCraft
  • CivilCraft
  64-bit

• Sun direction in model axes

  The sun's altitude, azimuth and direction for a solar hour, turned to the model's north.

  dir = east × dₓ + north × d_y, with d_z unchanged; ω = 15° × (solar hour − 12)

  Sun position and light on a tilted plane for solar pv-sun.js

  • BimCraft
  • CivilCraft
  64-bit

• Daily extraterrestrial radiation

  The energy on a horizontal plane above the atmosphere in one day.

  δ = 23.45° × sin(2π(284 + n) ÷ 365); ω_s = acos(−tan φ · tan δ); H₀ = 24 ÷ π × G_on ÷ 1000 × (cos φ cos δ sin ω_s + ω_s sin φ sin δ)

  Sun position and light on a tilted plane for solar pv-sun.js

  • BimCraft
  • CivilCraft
  64-bit

• Monthly diffuse fraction

  The share of a month's daily light that is diffuse, from the clearness index.

  ω_s ≤ 81.4°: 1.391 − 3.56 k + 4.189 k² − 2.137 k³; else 1.311 − 3.022 k + 3.427 k² − 1.821 k³

  Sun position and light on a tilted plane for solar pv-sun.js

  • BimCraft
  • CivilCraft
  64-bit

• Hourly share of the day's light

  The share of a day's total and diffuse light that falls in one hour.

  r_d = π ÷ 24 × (cos ω − cos ω_s) ÷ (sin ω_s − ω_s cos ω_s); r_t = (a + b cos ω) × r_d

  Sun position and light on a tilted plane for solar pv-sun.js

  • BimCraft
  • CivilCraft
  64-bit

• Hourly light from a typed monthly total

  Spreads a typed daily total over the hours and splits it into diffuse and direct light.

  I = H × r_t ÷ Σ r_t; I_d = min(I, H_d × r_d ÷ Σ r_d); DNI = min((GHI − DHI) ÷ cos z, 0.8 × G_on)

  Sun position and light on a tilted plane for solar pv-sun.js

  • BimCraft
  • CivilCraft
  64-bit

• Light on a tilted plane

  The direct, sky and ground-reflected light on a module plane in one hour.

  beam = DNI × cos θ; sky = DHI × (1 + cos β) ÷ 2; ground = GHI × ρ × (1 − cos β) ÷ 2; IAM = max(0, 1 − b₀(1 ÷ cos θ − 1))

  Sun position and light on a tilted plane for solar pv-sun.js

  • BimCraft
  • CivilCraft
  64-bit

• Site position and time zone

  The latitude, longitude, north direction and time zone used for the sun.

  time zone = round(longitude ÷ 15) unless given

  Solar arrays on the model pv-calc.js

  • BimCraft
  64-bit

• Model triangles in millimeters

  Every placed triangle of the model that can shade or carry modules.

  mm = mesh position × unit in mm

  Solar arrays on the model pv-calc.js

  • BimCraft
  32-bit in part

• Array tilt and power

  The tilt, azimuth and peak power recorded for a planned array.

  tilt = acos(clamp(n_z, −1, 1)) × 180 ÷ π; kWp = modules × Wp ÷ 1000

  Solar arrays on the model pv-calc.js

  • BimCraft
  64-bit

• Array definition stored in the file

  The text that records an array's plane, module size and module centers.

  normal, u, v: round to 1e-6; module centers and table corners: round to 0.1 mm

  Solar arrays on the model pv-calc.js

  • BimCraft
  64-bit

• Arrays read back from the file

  Rebuilds each array's modules and corners from its stored definition.

  corner = c ± u × across ÷ 2 ± v × along ÷ 2

  Solar arrays on the model pv-calc.js

  • BimCraft
  64-bit

• Module frames in the level's axes

  Turns module centers and the array's directions from model axes into the level's own axes for the stored solids.

  point′ = S⁻¹ · p; direction′ = S⁻¹ · d − S⁻¹ · 0

  Solar arrays on the model pv-calc.js

  • BimCraft
  64-bit

• Shade fraction of an array

  The shaded share of each array for every month and hour.

  fraction = Σ (table fraction × table samples) ÷ Σ samples

  Solar arrays on the model pv-calc.js

  • BimCraft
  64-bit

• Overcurrent device size

  The smallest standard device that is at least the required current.

  smallest x in the list with x ≥ amps − 1e-9

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

  • BimCraft
  64-bit

• 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

  • BimCraft
  64-bit

• 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

  • BimCraft
  64-bit

• 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

  • BimCraft
  64-bit

• 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

  • BimCraft
  64-bit

• 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

  • BimCraft
  64-bit

• 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

  • BimCraft
  • CivilCraft
  64-bit

• 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

  • BimCraft
  • CivilCraft
  64-bit

• 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

  • BimCraft
  • CivilCraft
  64-bit

• 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

  • BimCraft
  • CivilCraft
  64-bit

• 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

  • BimCraft
  • CivilCraft
  64-bit

• 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

  • BimCraft
  • CivilCraft
  64-bit

• Lowest and highest elevation

  The minimum and maximum elevation shown for a grid.

  Elevation grids read from GeoTIFF and ASCII files raster.js

  • BimCraft
  • CivilCraft
  64-bit

• 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

  • BimCraft
  • CivilCraft
  64-bit

• 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

  • BimCraft
  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

  • BimCraft
  32-bit, display only

• 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

  • BimCraft
  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

  • BimCraft
  64-bit

• 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

  • BimCraft
  64-bit

• 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

  • BimCraft
  64-bit

• 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

  • BimCraft
  64-bit

• 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

  • BimCraft
  64-bit

• 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

  • BimCraft
  64-bit

• 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

  • BimCraft
  64-bit

• 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

  • BimCraft
  64-bit

• 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

  • BimCraft
  64-bit

• 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

  • BimCraft
  64-bit

• 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

  • BimCraft
  64-bit

• 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

  • BimCraft
  64-bit

• 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

  • BimCraft
  64-bit

• 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

  • BimCraft
  Exact

• 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

  • BimCraft
  64-bit

• 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

  • BimCraft
  64-bit