Calculations

Calculations

• Profile point added by a click

  The station and elevation of a profile point placed in the profile view.

  station = Number(sta.toFixed(2)), clamped to the alignment; z = Number(z.toFixed(2))

  Values typed or picked in the main window civilcraft.js

  • CivilCraft
  64-bit

• Profile point moved by dragging

  The station and elevation of a profile point while it is dragged, as stored when released.

  station and z = Number(v.toFixed(2)); station kept 0.01 inside its neighbors

  Values typed or picked in the main window civilcraft.js

  • CivilCraft
  64-bit

• Elevation of a newly drawn pad

  The elevation a new pad starts at.

  z = Number(ground(mean of corners).toFixed(1))

  Values typed or picked in the main window civilcraft.js

  • CivilCraft
  64-bit

• Default curve radius at a new PI

  The radius given to each bend of a newly drawn alignment.

  r = min(R, ⌊half the shorter leg ÷ tan(Δ ÷ 2)⌋)

  Values typed or picked in the main window civilcraft.js

  • CivilCraft
  64-bit

• Ground elevation at a station

  The existing ground elevation read out at the cursor's station in the profile view.

  z = z_a + (z_b − z_a) × (s − s_a) ÷ (s_b − s_a)

  Values typed or picked in the main window civilcraft.js

  • CivilCraft
  64-bit

• Project units per file unit

  The factor that turns a spacing typed in project units into the file's own units.

  k = |f(c + d) − f(c)| ÷ d, c = middle of the file

  Terrain import and GeoTIFF export settings gis-terrain-ui.js

  • CivilCraft
  64-bit

• Default thinning spacing

  The spacing the dialog proposes so the import stays under the point limit.

  grid: cell × ⌈√(n ÷ (0.98 × cap))⌉; LiDAR: max(1.5 × √(area ÷ points), 1.1 × √(area ÷ cap)) rounded to a 1-2-5 step

  Terrain import and GeoTIFF export settings gis-terrain-ui.js

  • CivilCraft
  64-bit

• Points a grid import will make

  The number of cells read and of points or triangles made, shown before the import runs.

  count = ⌈columns ÷ step⌉ × ⌈rows ÷ step⌉; triangles = 2 × (⌈columns ÷ step⌉ − 1) × (⌈rows ÷ step⌉ − 1)

  Terrain import and GeoTIFF export settings gis-terrain-ui.js

  • CivilCraft
  64-bit

• LiDAR point into project coordinates

  Each kept LiDAR point's position and elevation as stored in the project.

  (x, y) → f(x, y); z → z × z factor

  Terrain import and GeoTIFF export settings gis-terrain-ui.js

  • CivilCraft
  64-bit

• Default GeoTIFF cell size

  The cell size proposed when a surface is exported as an elevation grid.

  cell = average triangle edge ÷ 2.5, rounded to a 1-2-5 step

  Terrain import and GeoTIFF export settings gis-terrain-ui.js

  • CivilCraft
  64-bit

• GeoTIFF grid size estimate

  The number of columns and rows the dialog says the export will have.

  nx = ⌈width ÷ cell⌉ + 1; ny = ⌈height ÷ cell⌉ + 1

  Terrain import and GeoTIFF export settings gis-terrain-ui.js

  • CivilCraft
  64-bit

• One slope line to the ground

  The point where a cut or fill slope leaving the pad edge meets the surface.

  f(d) = z + g·d − ground(p₀ + u·d); g = rate ÷ cut or −rate ÷ fill; find d with f(d) = 0

  Pad daylight lines and the graded surface grading.js

  • CivilCraft
  64-bit

• Rays round the pad

  The start, direction and climb rate of every slope line: square to each edge, fanned at convex corners, along the bisector at concave corners.

  turn = atan2(n₁ × n₂, n₁ · n₂); concave rate = cos(|turn| ÷ 2); wall mitre = thickness ÷ max(0.25, cos(|turn| ÷ 2))

  Pad daylight lines and the graded surface grading.js

  • CivilCraft
  64-bit

• Rays trimmed at a concave corner

  Drops edge rays that would reach past the line where two slopes meet in an inside corner.

  side(x, y) = b_x·(y − v_y) − b_y·(x − v_x); drop when the ray's ends have opposite signs

  Pad daylight lines and the graded surface grading.js

  • CivilCraft
  64-bit

• Pad, slopes and daylight line as breaklines

  The lines that go into the proposed surface for one pad: its edge, its daylight line and every slope line longer than 1e-6.

  Pad daylight lines and the graded surface grading.js

  • CivilCraft
  64-bit

• Proposed surface from ground and graded items

  Removes ground points and breaklines inside each graded region, adds the item's own, and triangulates again.

  Pad daylight lines and the graded surface grading.js

  • CivilCraft
  64-bit

• Do two segments cross

  The yes-or-no test used for self-crossing pads, self-crossing daylight lines and breaklines that cross a region.

  o(p, q, r) = (q − p) × (r − p); cross when both pairs of signs are opposite

  Pad daylight lines and the graded surface grading.js

  • CivilCraft
  64-bit

• Distance from a point to a polygon edge

  Whether a ground point lies on a daylight line.

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

  Pad daylight lines and the graded surface grading.js

  • CivilCraft
  64-bit

• Cut, fill and net volume

  The volumes reported between the existing and the proposed surface.

  fill = Σ (z₁ − z₀)·c² where z₁ > z₀; cut = Σ (z₀ − z₁)·c² otherwise; net = fill − cut; area = cells × c²

  Cut and fill volumes by the grid method grading.js

  • CivilCraft
  64-bit

• Default cell size

  Rounds the automatic cell size to 1, 2, 5 or 10 times a power of ten.

  p = 10^⌊log₁₀ v⌋; cell = {1, 2, 5, 10} × p

  Cut and fill volumes by the grid method grading.js

  • CivilCraft
  64-bit

• Elevation of a contour line

  The one elevation a line carries: its own z, or the z all its vertices share.

  Ground surface from contour lines and points ground-surface.js

  • CivilCraft
  64-bit

• Elevations by picking lines in order

  Gives the k-th picked line the elevation start + k × interval.

  z_k = start + k × interval

  Ground surface from contour lines and points ground-surface.js

  • CivilCraft
  64-bit

• Where two contour segments cross

  The crossing point of two segments, or none when they are parallel or only meet at an end.

  d = (q − p) × (s − r); t = (r − p) × (s − r) ÷ d; point = p + t·(q − p)

  Ground surface from contour lines and points ground-surface.js

  • CivilCraft
  64-bit

• Contour checks

  Lists lines with no elevation, elevations off the interval, duplicate lines and lines that cross.

  k = (z − base) ÷ interval; off the interval when |k − round(k)| > 1e-6

  Ground surface from contour lines and points ground-surface.js

  • CivilCraft
  64-bit

• Line simplification

  Removes contour vertices that lie within a tolerance of the line through their neighbors.

  distance = |(p − a) × (b − a)| ÷ |b − a|

  Ground surface from contour lines and points ground-surface.js

  • CivilCraft
  64-bit

• Placing by two known points

  The scale, rotation and shift that take two picked points to their real positions.

  k = |b₂ − a₂| ÷ |b − a|; rot = atan2(d₂) − atan2(d₁); x′ = k·(x cos rot − y sin rot) + t_x

  Ground surface from contour lines and points ground-surface.js

  • CivilCraft
  64-bit

• Points inside flat triangles

  An estimated elevation at the centroid of each triangle whose three corners are on one contour.

  z = z₀ − (z_apex − z₀) ÷ h_n × (h ÷ 3), averaged over contour edges; limited to z₀ ± interval ÷ 2

  Ground surface from contour lines and points ground-surface.js

  • CivilCraft
  64-bit

• Building the ground surface

  Thins the points when a spacing is given, triangulates with the breaklines, and repeats the flat-triangle fill-in up to three times.

  Ground surface from contour lines and points ground-surface.js

  • CivilCraft
  64-bit

• Catchment area

  The area of a catchment polygon in acres or hectares.

  A = |Σ (x_j + x_i)(y_j − y_i)| ÷ 2; ÷ 43560 for acres, ÷ 10000 for hectares

  Storm drainage: rational method, pipe sizing and grade lines hydro.js

  • CivilCraft
  64-bit

• Rainfall intensity

  The design rainfall intensity for a time of concentration.

  i = a ÷ (tc + b)^c

  Storm drainage: rational method, pipe sizing and grade lines hydro.js

  • CivilCraft
  64-bit

• Manning factor and gravity

  The unit factor in Manning's equation and the acceleration of gravity used for velocity head.

  k = 1 (m) or 1.486 (ft); g = 9.81 (m) or 32.174 (ft)

  Storm drainage: rational method, pipe sizing and grade lines hydro.js

  • CivilCraft
  64-bit

• Full-pipe capacity

  The flow and velocity of a circular pipe running full.

  Q = (k ÷ n) × A × R^(2/3) × √S; A = πD² ÷ 4; R = D ÷ 4

  Storm drainage: rational method, pipe sizing and grade lines hydro.js

  • CivilCraft
  64-bit

• Part-full pipe section

  The flow area, wetted perimeter and top width of a circular pipe flowing to a given depth.

  θ = 2·acos(1 − 2y ÷ D); A = D² ÷ 8 × (θ − sin θ); P = Dθ ÷ 2; T = D sin(θ ÷ 2)

  Storm drainage: rational method, pipe sizing and grade lines hydro.js

  • CivilCraft
  64-bit

• Normal depth

  The depth at which a pipe carries a given flow at its own slope.

  solve (k ÷ n) × A(y) × (A(y) ÷ P(y))^(2/3) × √S = Q for y

  Storm drainage: rational method, pipe sizing and grade lines hydro.js

  • CivilCraft
  64-bit

• Design flow in each pipe

  Accumulates C × A downstream, takes the longest time of concentration, and gives each pipe its flow.

  Q = ΣCA × i(tc) (cfs, acres); Q = ΣCA × i(tc) ÷ 360 (m³/s, hectares); travel = L ÷ V ÷ 60

  Storm drainage: rational method, pipe sizing and grade lines hydro.js

  • CivilCraft
  64-bit

• Pipe size

  The smallest standard diameter whose full-flow capacity is at least the design flow.

  Storm drainage: rational method, pipe sizing and grade lines hydro.js

  • CivilCraft
  64-bit

• Hydraulic and energy grade lines

  The water level and energy level at each end of each pipe and at each structure, from the outlet upstream.

  S_f = (Q·n ÷ (k·A·R^(2/3)))²; HGL_up = max(HGL_dn + S_f·L, invert + D) when full, else invert + y_n; h_v = V² ÷ 2g; structure = HGL_up + k_j·h_v

  Storm drainage: rational method, pipe sizing and grade lines hydro.js

  • CivilCraft
  64-bit

• Mesh with shared vertices

  Builds a triangle mesh in which points with the same coordinates become one vertex.

  IFC export: geometry and quantities gathered from the project ifc-civil-model.js

  • CivilCraft
  64-bit

• Surface area of a mesh

  The area of a corridor part or slope, as the sum of its triangles.

  area = Σ |(b − a) × (c − a)| ÷ 2

  IFC export: geometry and quantities gathered from the project ifc-civil-model.js

  • CivilCraft
  64-bit

• Vertical alignment segments

  Splits a design profile into constant grades and parabolic curves, clipped to the alignment, with each segment's start elevation and grades.

  IFC export: geometry and quantities gathered from the project ifc-civil-model.js

  • CivilCraft
  64-bit

• Alignment as a 3D polyline

  Samples the centerline into points with stations and design elevations.

  step = max(length ÷ 400, 1 m or 3 ft); angle limit 1°

  IFC export: geometry and quantities gathered from the project ifc-civil-model.js

  • CivilCraft
  64-bit

• Corridor parts and their areas

  Joins neighboring cross sections into surfaces per part and side, and measures each surface.

  area = mesh area; length = to station − from station

  IFC export: geometry and quantities gathered from the project ifc-civil-model.js

  • CivilCraft
  64-bit

• Pavement course solids

  A closed solid for each pavement course: the part's top edges lowered straight down by the depth of the course's top and bottom.

  z = z_edge − depth; depth of a course's top = Σ thickness of the courses above

  IFC export: geometry and quantities gathered from the project ifc-civil-model.js

  • CivilCraft
  64-bit

• Rail cross section in project units

  The outline of a rail (head, web, foot) from its section sizes in millimeters.

  k = 0.001 (m) or 0.001 ÷ 0.3048006096 (ft); head height = 0.27 h; foot height = 0.12 h

  IFC export: geometry and quantities gathered from the project ifc-civil-model.js

  • CivilCraft
  64-bit

• Rails, sleepers and ballast

  Places the rail outline on each section turned to the track's cross slope, and sets sleepers along each track at their spacing.

  o′ = o·cos(atan s) − z·sin(atan s); z′ = o·sin(atan s) + z·cos(atan s); sleeper k at distance k × spacing

  IFC export: geometry and quantities gathered from the project ifc-civil-model.js

  • CivilCraft
  64-bit

• Solid orientation

  Decides whether a closed mesh's triangles face outward, and flips them if not.

  V = Σ a · (b × c); flip when V < 0

  IFC export: geometry and quantities gathered from the project ifc-civil-model.js

  • CivilCraft
  64-bit

• Retaining wall solids and volume

  A closed solid for each wall run with its length, heights, face area and volume.

  volume = face area × thickness

  IFC export: geometry and quantities gathered from the project ifc-civil-model.js

  • CivilCraft
  64-bit

• Pad top, slopes and area

  The pad's top surface, its cut and fill slope surfaces and its plan area.

  area = |Σ (x_i·y_j − x_j·y_i)| ÷ 2

  IFC export: geometry and quantities gathered from the project ifc-civil-model.js

  • CivilCraft
  64-bit

• Superelevation event stations

  The stations at which lane slopes are written as superelevation events.

  IFC export: geometry and quantities gathered from the project ifc-civil-model.js

  • CivilCraft
  64-bit

• Structure floor and pipe sizes

  The floor level of a manhole or inlet and the pipe diameter and plan length written for the network.

  floor = sump level, else rim − 1.5 m or rim − 5 ft; D = size ÷ 1000 or ÷ 12; L = hypot(Δx, Δy)

  IFC export: geometry and quantities gathered from the project ifc-civil-model.js

  • CivilCraft
  64-bit