Calculations

Calculations

• Module DC power

  The power of one module at a given irradiance and cell temperature.

  P = Wp × G ÷ 1000 × (1 + γ × (T_cell − 25))

  Solar yield estimate pv-yield.js

  • BimCraft
  • CivilCraft
  64-bit

• Loss chain

  The share of the DC energy left after soiling, mismatch, wiring, downtime and the inverter.

  chain = (1 − soiling) × (1 − mismatch) × (1 − wiring) × (1 − availability) × inverter efficiency

  Solar yield estimate pv-yield.js

  • BimCraft
  • CivilCraft
  64-bit

• Power in one hour

  The light on the array, the cell temperature and the DC and AC power for one hour of a month's representative day.

  G = beam × (1 − shade) + sky + ground; P = n × max(0, module power); AC before clipping = P ÷ 1000 × chain

  Solar yield estimate pv-yield.js

  • BimCraft
  • CivilCraft
  64-bit

• Monthly figures

  A month's light, shade loss and DC energy from its representative day.

  month = day × days in month; shade loss % = (unshaded − shaded) ÷ unshaded × 100

  Solar yield estimate pv-yield.js

  • BimCraft
  • CivilCraft
  64-bit

• Inverter clipping and monthly AC energy

  The AC energy of each month after the inverter's rating limits the hourly power.

  scale = P_ac ÷ Σ P when Σ P > P_ac; month AC = Σₕ P × scale × days, rounded to 0.1 kWh

  Solar yield estimate pv-yield.js

  • BimCraft
  • CivilCraft
  64-bit

• Annual energy, specific yield and performance ratio of an array

  An array's yearly DC and AC energy, kWh per kWp and performance ratio.

  AC = Σ rounded months; specific yield = AC ÷ kWp; PR = AC ÷ (kWp × POA)

  Solar yield estimate pv-yield.js

  • BimCraft
  • CivilCraft
  64-bit

• Plant totals

  The energy, specific yield, performance ratio, clipping and shade loss of all arrays together.

  PR = Σ AC ÷ Σ(kWp × POA); clipped % = clipped ÷ unclipped × 100

  Solar yield estimate pv-yield.js

  • BimCraft
  • CivilCraft
  64-bit

• Mesh handed to the solid kernel

  Welds the mesh's corners and passes it to manifold-3d.

  weld grid = 10⁻⁶ × max(Δx, Δy, Δz); positions → Float32Array

  IFC openings, clippings and half-space cuts ifc/geo-bool.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  32-bit in part

• Boolean of two solids

  The difference, union or intersection of two element meshes.

  c = center of a's box; R = (a − c) OP (b − c); result = R + c

  IFC openings, clippings and half-space cuts ifc/geo-bool.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  32-bit in part

• Element minus all its openings

  Subtracts every opening from an element, one after another.

  A₀ = base − c; Aᵢ = Aᵢ₋₁ − (cutterᵢ − c); result = Aₙ + c

  IFC openings, clippings and half-space cuts ifc/geo-bool.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  32-bit in part

• Face planes of a convex cutter

  Finds the outward planes of a cutter and decides whether it is convex.

  n = (b − a) × (c − a) ÷ |…|; d = n · a; convex when n · p − d ≤ 10 ε for every corner p

  IFC openings, clippings and half-space cuts ifc/geo-bool.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Polygon split by a plane

  Cuts a convex polygon into the part in front of a plane and the part behind it.

  t = dₐ ÷ (dₐ − d_b); x = a + (b − a) t

  IFC openings, clippings and half-space cuts ifc/geo-bool.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Mesh clipped by a plane

  Keeps the part of a mesh on one side of a plane and closes the cut.

  dᵢ = (pᵢ − p) · n; ε = 10⁻⁹ × (d_max − d_min); cut point = a + (b − a) dₐ ÷ (dₐ − d_b)

  IFC openings, clippings and half-space cuts ifc/geo-bool.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Cap of a cut

  Joins the cut segments into loops, sorts outer loops from holes and fills them.

  key = round(x ÷ tol), round(y ÷ tol), round(z ÷ tol); area = ½ |Σ (xᵢ yᵢ₊₁ − xᵢ₊₁ yᵢ)|

  IFC openings, clippings and half-space cuts ifc/geo-bool.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Half-space cut

  Removes the part of an element behind a plane, optionally only inside a polygon boundary.

  L = 4 × max(1, box diagonal) + |P₀ − box min|; prism height = 2 L

  IFC openings, clippings and half-space cuts ifc/geo-bool.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  32-bit in part

• Vertex data of one geometry

  Returns a geometry's positions and normals for drawing and for measuring.

  IFC geometry handed to the apps ifc/api.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  32-bit in part

• Placement matrix of each piece

  The matrix that takes a geometry's vertices to model space in meters, Y up.

  M = C × Y-up × scale(u) × placement

  IFC geometry handed to the apps ifc/api.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Shift to the origin

  Finds the translation that brings the model near the origin.

  c = (box min + box max) ÷ 2 of the first element; C = translate(−(Y-up × scale(u) × placement × c))

  IFC geometry handed to the apps ifc/api.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• File units to meters, Z up to Y up

  Scales a placement by the file's length unit and turns its axes.

  M′ = Y-up × scale(u) × M

  IFC geometry handed to the apps ifc/api.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Unit sizes in meters

  The length of a meter, a foot and a US survey foot used for elevations.

  ft = 0.3048 m; US survey ft = 1200 ÷ 3937 m

  GIS import: reprojection and elevation units gis-read.js

  • CivilCraft
  Exact

• Features placed in the project

  Reprojects every vertex of every layer and scales its elevation.

  z′ = z × (source unit in m ÷ project unit in m)

  GIS import: reprojection and elevation units gis-read.js

  • CivilCraft
  64-bit

• Middle of the data in longitude and latitude

  Finds where the imported data lies, to suggest a coordinate system near it.

  c = (min + max) ÷ 2 of the bounding box

  GIS import: reprojection and elevation units gis-read.js

  • CivilCraft
  64-bit

• Survey points given as latitude and longitude

  Converts point-file rows in degrees to project coordinates.

  GIS import: reprojection and elevation units gis-read.js

  • CivilCraft
  64-bit

• Default thresholds

  The heights the filter uses when the caller gives none.

  h₀ = 0.3 × cell; h_max = 6 × cell; low noise = slope × cell × 3 + 3 × h₀

  Ground points from an unclassified point cloud ground-classify.js

  • CivilCraft
  64-bit

• Lowest point per cell

  Sorts the points into grid cells and keeps the lowest of each.

  column = ⌊(x − minₓ) ÷ cell⌋; row = ⌊(y − min_y) ÷ cell⌋

  Ground points from an unclassified point cloud ground-classify.js

  • CivilCraft
  64-bit

• Stray low points

  Drops single points that lie far below their neighbors.

  stray when median(neighbors) − z > low-noise limit

  Ground points from an unclassified point cloud ground-classify.js

  • CivilCraft
  64-bit

• Opening with growing windows

  Marks cells that stand above the opened surface as objects, round by round.

  wₖ = 2ᵏ + 1; dhₖ = min(h_max, slope × (wₖ − wₖ₋₁) × cell + h₀); object when z − opened > dhₖ

  Ground points from an unclassified point cloud ground-classify.js

  • CivilCraft
  64-bit

• Morphological opening

  The minimum, then the maximum, over a square window around each cell.

  Ground points from an unclassified point cloud ground-classify.js

  • CivilCraft
  64-bit

• Coordinates read from a row

  Takes the northing, easting and elevation of one line of a point file.

  Survey point files: reading and writing points.js

  • CivilCraft
  64-bit

• Points written as a PNEZD file

  Writes point number, northing, easting, elevation and description, comma separated.

  N, E and Z written with dec decimals (3 by default)

  Survey point files: reading and writing points.js

  • CivilCraft
  64-bit

• Point count per group

  Counts the points of each description group.

  Survey point files: reading and writing points.js

  • CivilCraft
  Exact

• Grades and vertical curves

  Builds the grades between PVIs and the curve at each interior PVI.

  g = Δz ÷ Δsta; A = (g₂ − g₁) × 100; L = K × |A|; z_BVC = z_PVI − g₁ × L ÷ 2; x_high/low = −g₁ × L ÷ (g₂ − g₁)

  Vertical profile: grades and parabolic curves profile.js

  • CivilCraft
  64-bit

• Design elevation at a station

  The profile's elevation at any station.

  z = z_BVC + g₁ × x + (g₂ − g₁) × x² ÷ (2L), x = sta − BVC; on a tangent z = zᵢ + g × (sta − staᵢ)

  Vertical profile: grades and parabolic curves profile.js

  • CivilCraft
  64-bit

• Grade at a station

  The profile's slope at any station.

  g = g₁ + (g₂ − g₁) × (sta − BVC) ÷ L

  Vertical profile: grades and parabolic curves profile.js

  • CivilCraft
  64-bit

• Existing ground along the alignment

  Samples the surface's elevation at regular stations and at the alignment's key stations.

  step = length ÷ 1000, at least 0.5; stations: start, start + step, …, end, plus key stations

  Vertical profile: grades and parabolic curves profile.js

  • CivilCraft
  64-bit

• Stand-in ground for a road with no survey

  The elevation and extent of the flat ground a corridor is drawn on when the project has no surface.

  z = mean of the PVI elevations, rounded to 0.01; margin = (60 m or 200 ft) + 6 × (z_max − z_min)

  Project: stand-in ground, volumes and saved points project.js

  • CivilCraft
  64-bit

• Cut and fill inside the daylight lines

  The total cut and fill and the figures per graded item.

  Project: stand-in ground, volumes and saved points project.js

  • CivilCraft
  64-bit

• Points in the project file

  Writes each survey point to the .civilcraft.json file.

  Project: stand-in ground, volumes and saved points project.js

  • CivilCraft
  64-bit

• Default rate table

  The rates by radius and the relative gradient a new corridor starts with.

  Superelevation: runoff, runout and lane slopes superelev.js

  • CivilCraft
  64-bit

• Rate for a radius

  Looks up the superelevation rate of a curve.

  Superelevation: runoff, runout and lane slopes superelev.js

  • CivilCraft
  64-bit

• Runoff, runout and transition stations

  The lengths and stations of the transition into and out of each curve.

  L_r = lane × e ÷ Δ; L_t = (NC ÷ e) × L_r; without a spiral: level at TS − ⅔L_r, full at TS + ⅓L_r

  Superelevation: runoff, runout and lane slopes superelev.js

  • CivilCraft
  64-bit

• Outside lane slope through a transition

  The cross slope of the outside lane at a station.

  runout: NC − NC × (x − nc₀) ÷ L_t; runoff: −e × (x − lc₀) ÷ L_r; result = max(up, down, −e)

  Superelevation: runoff, runout and lane slopes superelev.js

  • CivilCraft
  64-bit

• Lane slopes at a station

  The fall-away slope of the left and right lanes.

  inside = max(NC, −outside)

  Superelevation: runoff, runout and lane slopes superelev.js

  • CivilCraft
  64-bit

• Line taken from the team

  Turns shared geometry into feature line points in the drawing's unit.

  k = 1 (same unit), 0.3048 (ft → m) or 1 ÷ 0.3048 (m → ft); p′ = p × k

  Shared feature lines: units and geometry team-lines.js

  • CivilCraft
  64-bit

• Line sent to the team

  Turns a feature line into the points that are shared.

  Shared feature lines: units and geometry team-lines.js

  • CivilCraft
  64-bit

• One point into its cell

  Decides whether an incoming point is kept, replaces the cell's point, or is dropped.

  i = ⌊(x − oₓ) ÷ cell⌋; key = i × 2³² + (j + 2³¹); nearest: d² = (fₓ − i − ½)² + (f_y − j − ½)²

  Thinning point clouds to a spacing thin.js

  • CivilCraft
  64-bit

• The thinned points

  Returns one point per occupied cell.

  average mode: x̄ = Σx ÷ n, ȳ = Σy ÷ n, z̄ = Σz ÷ n

  Thinning point clouds to a spacing thin.js

  • CivilCraft
  64-bit

• Grid step for a spacing

  How many grid nodes to skip so an elevation grid is thinned to about the spacing asked for.

  n = max(1, round(spacing ÷ cell size))

  Thinning point clouds to a spacing thin.js

  • CivilCraft
  64-bit

• Estimate of points kept

  Tells the import dialog about how many points a thinning will keep.

  kept ≈ Σ min(points × f, cell area × f ÷ spacing² + 1), f = part of the coarse cell inside the area

  Thinning point clouds to a spacing thin.js

  • CivilCraft
  64-bit

• Value of a number row

  The number handed to the app when a person changes a number box.

  v = min(max, max(min, typed value))

  Numbers typed into the property grid app-propgrid.js Every app
  64-bit