Calculations

Calculations

• Sun azimuth and altitude

  The sun's direction and height above the horizon at a moment and a place.

  JD = ms ÷ 86 400 000 + 2 440 587.5; T = (JD − 2 451 545) ÷ 36 525; cos Z = sin φ·sin δ + cos φ·cos δ·cos H

  Sun position drive.js

  • CivilCraft
  64-bit

• Atmospheric refraction

  The lift of the sun's apparent altitude by the atmosphere, added to the geometric altitude.

  h > 5°: 58.1 ÷ tan h − 0.07 ÷ tan³h + 0.000086 ÷ tan⁵h seconds of arc

  Sun position drive.js

  • CivilCraft
  64-bit

• Unit vector toward the sun

  The sun's direction as east, north and up components.

  (cos h·sin a, cos h·cos a, sin h)

  Sun position drive.js

  • CivilCraft
  64-bit

• Ground samples inside the area

  A grid of ground elevations inside the polygon, each standing for one cell of ground.

  cell = √(bounding box area ÷ 20 000) unless given

  Earthwork balance and haul plan earthwork.js

  • CivilCraft
  64-bit

• Cut and fill volumes

  Cut, fill, usable cut and the net at a design level.

  fill = area × Σ max(design − ground, 0); cut = area × Σ max(ground − design, 0); net = cut × factor − fill

  Earthwork balance and haul plan earthwork.js

  • CivilCraft
  64-bit

• Balanced level

  The design level at which usable cut equals fill.

  Earthwork balance and haul plan earthwork.js

  • CivilCraft
  64-bit

• Design plane

  The design elevation at a point for a level and two grades.

  z = z₀ + gx·(x − cx) + gy·(y − cy)

  Earthwork balance and haul plan earthwork.js

  • CivilCraft
  64-bit

• Free-haul moment

  The volume moved times the distance between the centroid of cut and the centroid of fill.

  moment = min(cut × factor, fill) × |centroid(cut) − centroid(fill)|

  Earthwork balance and haul plan earthwork.js

  • CivilCraft
  64-bit

• Best tilt

  The level and tilt, within the grade limit, that balance with the least haul moment.

  Earthwork balance and haul plan earthwork.js

  • CivilCraft
  64-bit

• Blocks of cut and fill

  Cells grouped into blocks, each with its volume and its volume-weighted center.

  center = Σ (p × v) ÷ Σ v

  Earthwork balance and haul plan earthwork.js

  • CivilCraft
  64-bit

• Minimum-cost transport

  How much goes from each block of cut to each block of fill at the least total volume times distance.

  Earthwork balance and haul plan earthwork.js

  • CivilCraft
  64-bit

• Haul plan totals

  Volume moved on site, total haul, average haul distance, and what is left to take away or bring in.

  haul = Σ volume × distance; average = haul ÷ moved

  Earthwork balance and haul plan earthwork.js

  • CivilCraft
  64-bit

• Earthwork balancer run

  The volumes at the pad's present level, the balanced level, the tilt and the haul plan for one pad.

  factor = 1 + percent ÷ 100; cell area = cell²

  Earthwork, route and pond tools: values stored and exported eg-ui.js

  • CivilCraft
  64-bit

• Balanced level written to the pad

  The pad's level, and its corner elevations when it tilts, as stored in the project.

  z stored = Number(z.toFixed(3))

  Earthwork, route and pond tools: values stored and exported eg-ui.js

  • CivilCraft
  64-bit

• Haul plan CSV

  The haul flows exported as a CSV file.

  Earthwork, route and pond tools: values stored and exported eg-ui.js

  • CivilCraft
  64-bit

• Alignment from a found route

  The PIs of a new alignment from the route's points, with a curve radius at each bend.

  r = min(R, min(l₁, l₂) ÷ (2·tan(Δ/2))), stored to 2 decimals

  Earthwork, route and pond tools: values stored and exported eg-ui.js

  • CivilCraft
  64-bit

• Route ends picked in the plan

  The start and end of a route search as taken from two picked points.

  x, y = Number(v.toFixed(3))

  Earthwork, route and pond tools: values stored and exported eg-ui.js

  • CivilCraft
  64-bit

• Sized orifice written to the pond

  The orifice diameter found for the target outflow, as stored in the pond.

  diameter stored = Number((d ÷ L).toFixed(3))

  Earthwork, route and pond tools: values stored and exported eg-ui.js

  • CivilCraft
  64-bit

• Pond hydrograph CSV

  Inflow, outflow and stage against time exported as a CSV file.

  Earthwork, route and pond tools: values stored and exported eg-ui.js

  • CivilCraft
  64-bit

• Survey points for progress checks

  Ground points read from a LAS, LAZ, CSV or text file and turned into a surface.

  LAS thinning cell = max(0.5, √(extent area ÷ 400 000)) unless a spacing is given

  Earthwork, route and pond tools: values stored and exported eg-ui.js

  • CivilCraft
  64-bit

• Three-decimal rounding of tool results

  The rounding applied to nearly every number a tool returns to an assistant or script.

  r3(v) = round(v × 1000) ÷ 1000

  Earthwork, route and pond tools: values stored and exported eg-agent.js

  • CivilCraft
  64-bit

• Volumes in report units

  Volumes converted to cubic yards or cubic meters for a tool's answer.

  cubic yards = cubic feet ÷ 27; from cubic meters: ÷ 0.028316846592 ÷ 27

  Earthwork, route and pond tools: values stored and exported eg-agent.js

  • CivilCraft
  64-bit

• Rain results in inches and cubic feet per second

  Depths and flows from the rain solver converted from meters for a feet project.

  inches = meters × 39.3700787; ft³/s = m³/s ÷ 0.028316846592

  Earthwork, route and pond tools: values stored and exported eg-agent.js

  • CivilCraft
  64-bit

• Pad level set by an assistant

  A pad's level and, for a tilted pad, its corner elevations, as stored in the project.

  z stored = r3(level); corner z = r3(level + gx·(x − cx) + gy·(y − cy))

  Earthwork, route and pond tools: values stored and exported eg-agent.js

  • CivilCraft
  64-bit

• Alignment from route points

  The PIs of an alignment made by an assistant from route points, with curve radii.

  r = min(R, min(l₁, l₂) ÷ (2·tan(Δ/2))), stored to 3 decimals

  Earthwork, route and pond tools: values stored and exported eg-agent.js

  • CivilCraft
  64-bit

• Orifice sized by an assistant

  The orifice diameter found for an allowed outflow, as used for the reported run.

  diameter = r3(d ÷ L)

  Earthwork, route and pond tools: values stored and exported eg-agent.js

  • CivilCraft
  64-bit

• Arc from two points and a bulge

  The center, radius, start angle, sweep and length of the arc between two vertices.

  k = (1 − b²) ÷ (4b); center = chord middle + k·(−Δy, Δx); r = c·(1 + b²) ÷ (4|b|); sweep = 4·atan(b); L = r·|sweep|

  Feature line grades, arcs, offsets and crossings featureline.js

  • CivilCraft
  64-bit

• Bulge of an arc through three points

  The bulge of the arc drawn from a start, through a middle point, to an end.

  sweep = 2·(π − angle at the middle point); bulge = sign × tan(sweep ÷ 4)

  Feature line grades, arcs, offsets and crossings featureline.js

  • CivilCraft
  64-bit

• Bulge for a typed radius

  The bulge of the shorter arc of a given radius between two vertices.

  Δ = 2·asin(c ÷ 2r); bulge = ±tan(Δ ÷ 4)

  Feature line grades, arcs, offsets and crossings featureline.js

  • CivilCraft
  64-bit

• Point and direction along a segment

  The plan point and travel direction at a fraction of a straight or arc segment.

  arc: p = c + r·(cos θ, sin θ), θ = a₀ + sweep × u

  Feature line grades, arcs, offsets and crossings featureline.js

  • CivilCraft
  64-bit

• Segment lengths and grades

  Each segment's plan length, chord, 3D length, rise and grade.

  length = chord or r·|sweep|; 3D length = √(L² + Δz²); grade = Δz ÷ L

  Feature line grades, arcs, offsets and crossings featureline.js

  • CivilCraft
  64-bit

• Stations along a feature line

  The plan distance from the start to each vertex.

  Feature line grades, arcs, offsets and crossings featureline.js

  • CivilCraft
  64-bit

• Elevation from a grade

  The far vertex of a segment moved to the elevation a typed grade gives.

  z₂ = z₁ + grade × length

  Feature line grades, arcs, offsets and crossings featureline.js

  • CivilCraft
  64-bit

• One grade between two vertices

  The vertices between two chosen ones placed on a single grade.

  z = z₀ + (z₁ − z₀) × (s − s₀) ÷ L

  Feature line grades, arcs, offsets and crossings featureline.js

  • CivilCraft
  64-bit

• Stepped offset

  A copy of the line moved sideways with mitred corners and raised by a height or a cross slope.

  corner shift = bisector × d ÷ cos(half angle); z + Δz, or z + |d| × slope

  Feature line grades, arcs, offsets and crossings featureline.js

  • CivilCraft
  64-bit

• Straight segment against an alignment element

  Where a straight feature line segment crosses a line or arc of the alignment, with the station.

  line: 2×2 solve by cross products; arc: A·t² + B·t + C = 0, t = (−B ± √(B² − 4AC)) ÷ 2A

  Feature line grades, arcs, offsets and crossings featureline.js

  • CivilCraft
  64-bit

• Arc segment against an alignment element

  Where an arc of a feature line crosses a line or arc of the alignment.

  two circles: along = (r₁² − r₂² + d²) ÷ 2d; h = √(r₁² − along²)

  Feature line grades, arcs, offsets and crossings featureline.js

  • CivilCraft
  64-bit

• Feature line read from a file

  The vertices kept when a feature line is read from a project file or a drawing.

  Feature line grades, arcs, offsets and crossings featureline.js

  • CivilCraft
  64-bit

• Elevations of a newly drawn line

  The elevation each vertex of a new feature line gets.

  Feature line grades, arcs, offsets and crossings features-ui.js

  • CivilCraft
  64-bit

• Elevation and grade boxes

  A typed vertex elevation or segment grade applied to the line.

  grade = typed percent ÷ 100

  Feature line grades, arcs, offsets and crossings features-ui.js

  • CivilCraft
  64-bit

• Offset distance and amount

  The typed offset distance and height or slope passed to the stepped offset.

  slope = typed percent ÷ 100

  Feature line grades, arcs, offsets and crossings features-ui.js

  • CivilCraft
  64-bit

• Number of pieces for an arc

  How many straight pieces draw an arc within the tolerance.

  step = min(2·acos(1 − tol ÷ r), 5°); pieces = ⌈|sweep| ÷ step⌉, from 1 to 720

  Feature line arcs as straight pieces featureline.js

  • CivilCraft
  64-bit

• Line as straight pieces

  The feature line with every arc replaced by vertices on the arc.

  p = c + r·(cos θ, sin θ), θ = a₀ + sweep × s ÷ k; z = z_a + (z_b − z_a) × s ÷ k

  Feature line arcs as straight pieces featureline.js

  • CivilCraft
  64-bit

• Closed design line as a grading item

  The outline and the single elevation a closed design feature line passes to grading.

  z = Σ vertex z ÷ number of vertices

  Feature line arcs as straight pieces featureline.js

  • CivilCraft
  64-bit

• Feature line written to DWG or DXF

  The 3D polyline and the extended data that records which runs of pieces were arcs.

  Feature line arcs as straight pieces featureline.js

  • CivilCraft
  64-bit

• Feature line read back from DWG or DXF

  The feature line rebuilt from a polyline and its extended data.

  Feature line arcs as straight pieces featureline.js

  • CivilCraft
  64-bit

• Crossings with an alignment

  Every place a feature line crosses the centerline, with its station and elevation.

  z = z_a + t × Δz

  Feature line arcs as straight pieces featureline.js

  • CivilCraft
  64-bit

• Stretches running beside an alignment

  The parts of a feature line within a given distance of the centerline, as station and elevation for a profile view.

  Feature line arcs as straight pieces featureline.js

  • CivilCraft
  64-bit

• Project units to meters

  The factor that takes a project length to meters for every engine in this file.

  feet: 0.3048; meters: 1

  Running saved geotechnical, survey, pit and link items geo-run.js

  • CivilCraft
  64-bit

• Soil profile along a section

  The borings in meters, the layers between them, and the layer stack at evenly spaced stations.

  stations = max(2, round(length ÷ step)), default step = max(length ÷ 40, 0.5 m)

  Running saved geotechnical, survey, pit and link items geo-run.js

  • CivilCraft
  64-bit