Calculations

Calculations

• Layer elevations

  The top and bottom elevation and the thickness of each layer of a boring.

  top = z − from; bottom = z − to; thickness = to − from

  Boring logs and the soil profile between borings geotech.js

  • CivilCraft
  64-bit

• SPT blow count corrections

  N60 and (N1)60 from a field blow count.

  N60 = N × ER ÷ 60 × CB × CS × CR; CN = min(1.7, √(101.325 ÷ σ′v)); (N1)60 = CN × N60

  Boring logs and the soil profile between borings geotech.js

  • CivilCraft
  64-bit

• Boring projected onto the section line

  The station along the section and the offset from it of a boring.

  t = ((p − a)·(b − a)) ÷ |b − a|², clamped to 0…1; station = length so far + t·|b − a|

  Boring logs and the soil profile between borings geotech.js

  • CivilCraft
  64-bit

• Soil profile between borings

  The polygon of each soil unit between neighboring borings, the ground line and the water line.

  pinch-out point = ((s₁ + s₂) ÷ 2, (top + bottom) ÷ 2)

  Boring logs and the soil profile between borings geotech.js

  • CivilCraft
  64-bit

• Layer stack at a station

  The top and bottom of every soil unit at one station of the profile.

  z = z_a + (s − s_a) ÷ (s_c − s_a) × (z_c − z_a)

  Boring logs and the soil profile between borings geotech.js

  • CivilCraft
  64-bit

• Signed area of a ring

  The area of a ring, positive when it runs counter-clockwise.

  area = Σ (xᵢ·yᵢ₊₁ − xᵢ₊₁·yᵢ) ÷ 2

  GIS feature geometry gis-geom.js

  • CivilCraft
  64-bit

• Point inside a ring

  Whether a point lies inside a ring.

  GIS feature geometry gis-geom.js

  • CivilCraft
  64-bit

• Rings sorted into polygons and holes

  Which rings are outlines and which are holes, and which outline each hole belongs to.

  GIS feature geometry gis-geom.js

  • CivilCraft
  64-bit

• Coordinates through a conversion

  Every vertex of a geometry passed through a function of x and y, keeping z.

  GIS feature geometry gis-geom.js

  • CivilCraft
  64-bit

• Elevations through a conversion

  The z of every vertex passed through a function, for unit conversion.

  GIS feature geometry gis-geom.js

  • CivilCraft
  64-bit

• Layers moved to a new coordinate system

  Every GIS layer's coordinates converted when the project's system changes.

  project → grid of the old system → grid of the new system → project

  GIS feature geometry gis-layers.js

  • CivilCraft
  64-bit

• Attribute value as a label

  The text drawn on the plan for a feature's attribute value.

  number shown = +v.toFixed(3)

  GIS feature geometry gis-layers.js

  • CivilCraft
  64-bit

• Label point of a polygon

  The centroid of a polygon's largest ring, where its label is placed.

  cx = Σ (xᵢ + xᵢ₊₁)·cᵢ ÷ (3·Σ cᵢ), cᵢ = xᵢ·yᵢ₊₁ − xᵢ₊₁·yᵢ

  GIS feature geometry gis-layers.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

• Lengths, bearings, grades and area

  Every number the Measure tool shows for a picked line or shape.

  L = hypot(Δx, Δy); bearing = atan2(Δy, Δx); grade % = Δz ÷ L × 100; L₃ = hypot(L, Δz); area = |Σ (x_i·y_j − x_j·y_i)| ÷ 2

  Measure tool measure.js

  • CivilCraft
  64-bit

• Between two points on a profile

  The horizontal distance, height difference, straight-line distance and grade between two profile points.

  dx = |ch_b − ch_a|; dz = z_b − z_a; slope distance = hypot(dx, dz); grade % = dz ÷ dx × 100

  Measure tool measure.js

  • CivilCraft
  64-bit

• Angle from degrees, minutes and seconds

  Reads an angle typed as degrees, minutes and seconds or as decimal degrees.

  degrees = d + m ÷ 60 + s ÷ 3600

  Parcels: deed calls, closure, area and legal description parcels.js

  • CivilCraft
  64-bit

• Bearing to direction

  Turns a quadrant bearing or an azimuth into a direction in radians from east, counter-clockwise.

  direction = (90° − azimuth) × π ÷ 180, wrapped to 0…2π

  Parcels: deed calls, closure, area and legal description parcels.js

  • CivilCraft
  64-bit

• Central angle of a curve call

  The central angle of a deed curve from its arc length, or as typed.

  Δ = L ÷ R

  Parcels: deed calls, closure, area and legal description parcels.js

  • CivilCraft
  64-bit

• Traverse and misclosure

  The corners reached by the calls, the gap back to the start, the total length and the precision ratio.

  p ← p + d·(cos θ, sin θ); chord = 2R·sin(Δ ÷ 2); misclosure = |end − start|; precision = length ÷ misclosure

  Parcels: deed calls, closure, area and legal description parcels.js

  • CivilCraft
  64-bit

• Curve from a bulge

  The radius, length, central angle, chord, tangent directions and center of a curved course.

  Δ = 4·atan|b|; R = chord ÷ (2·sin(Δ ÷ 2)); L = R × Δ; center = start + R·(cos, sin)(dir_in ± 90°)

  Parcels: deed calls, closure, area and legal description parcels.js

  • CivilCraft
  64-bit

• Courses of a parcel

  Each side of the parcel as a line (direction and distance) or a curve.

  direction = atan2(Δy, Δx); distance = hypot(Δx, Δy)

  Parcels: deed calls, closure, area and legal description parcels.js

  • CivilCraft
  64-bit

• Parcel area

  The area of the parcel, with curved sides counted exactly.

  2A = Σ (x_i·y_j − x_j·y_i) + Σ ± R²·(Δ − sin Δ); area = |2A| ÷ 2

  Parcels: deed calls, closure, area and legal description parcels.js

  • CivilCraft
  64-bit

• Perimeter

  The length round the parcel.

  perimeter = Σ line distances + Σ curve lengths

  Parcels: deed calls, closure, area and legal description parcels.js

  • CivilCraft
  64-bit

• Area in words

  The area as square units with acres or hectares.

  acres = sq ft ÷ 43560; hectares = sq m ÷ 10000

  Parcels: deed calls, closure, area and legal description parcels.js

  • CivilCraft
  64-bit

• Legal description

  A draft description: the point of beginning, each course, and the area.

  Parcels: deed calls, closure, area and legal description parcels.js

  • CivilCraft
  64-bit

• Course and area labels

  The bearing and distance text along each side and the area text at the middle.

  Parcels: deed calls, closure, area and legal description parcels.js

  • CivilCraft
  64-bit

• Bulge from a typed radius

  Turns a radius typed for one side of a parcel into the stored curve.

  bulge = ± tan(asin(chord ÷ 2R) ÷ 2)

  Parcels: deed calls, closure, area and legal description parcels-ui.js

  • CivilCraft
  64-bit

• Does the traverse close

  Decides whether typed deed calls return to the start, in which case the last point is dropped and the parcel closes on its first corner.

  closes when misclosure ≤ 0.0005 × max(1, length ÷ 1000)

  Parcels: deed calls, closure, area and legal description parcels-ui.js

  • CivilCraft
  64-bit

• Gravity and Manning constant per unit system

  The gravity and the Manning equation constant every river calculation uses.

  m: k = 1, g = 9.80665; ft: k = 1.486, g = 32.174

  River model: stations, cut sections and reach lengths river.js

  • CivilCraft
  64-bit

• River station of a point

  The station of a point, measured along the centerline from its downstream end, and its offset to the side.

  rs = L − d

  River model: stations, cut sections and reach lengths river.js

  • CivilCraft
  64-bit

• Cross-section from a cut line

  Turns a line drawn across the river into a cross-section: station, ground points by offset, and first bank positions.

  rs = round₆(L − d_crossing); o = round₆(offset); banks = lowest point ± bank distance, clipped to the section

  River model: stations, cut sections and reach lengths river.js

  • CivilCraft
  64-bit

• Sections at a spacing along the centerline

  Cuts square cross-sections every set distance along the centerline and at both ends.

  dₖ = k × spacing while k × spacing < L − 1e-9; rs = round₆(L − dₖ)

  River model: stations, cut sections and reach lengths river.js

  • CivilCraft
  64-bit

• Reach lengths between sections

  The channel and overbank distances from each section to the next one downstream.

  channel = rsᵢ − rsᵢ₋₁; overbank = √(Δx² + Δy²) between the middles of the overbank parts of the two cut lines

  River model: stations, cut sections and reach lengths river.js

  • CivilCraft
  64-bit

• Flow at a station

  The flow that applies at a station, from the profile's flow and its flow changes.

  River model: stations, cut sections and reach lengths river.js

  • CivilCraft
  64-bit

• First guess of the boundary slope

  The slope offered for a normal-depth boundary when one is first chosen, from the lowest points of the end sections.

  S = (z_min upstream − z_min downstream) ÷ (rs upstream − rs downstream), to 3 significant digits; 0.001 when S ≤ 1e-5

  River model: stations, cut sections and reach lengths river-ui.js

  • CivilCraft
  64-bit

• Sample stations

  The stations where sections are cut: every multiple of the step, both ends, the curve ends and any extra stations.

  sta = round₆(k × step) for whole k; neighbors closer than 1e-6 merged

  Cross sections and end-area volumes along an alignment sections.js

  • CivilCraft
  64-bit

• Sample line at a station

  The two ends of the line square to the alignment at a station.

  right = (sin dir, −cos dir); a = c − right × left; b = c + right × right offset

  Cross sections and end-area volumes along an alignment sections.js

  • CivilCraft
  64-bit

• Surface along a sample line

  The ground or design line along a sample line, with a point at every triangle edge it crosses.

  z at a + (b − a)·t for every edge-crossing parameter t; o = offA + (offB − offA)·t

  Cross sections and end-area volumes along an alignment sections.js

  • CivilCraft
  64-bit

• Segment crossing parameter

  Where one segment crosses another, as a fraction along the first.

  den = r × s; t = ((q − p) × s) ÷ den; u = ((q − p) × r) ÷ den

  Cross sections and end-area volumes along an alignment sections.js

  • CivilCraft
  64-bit

• Elevation of a section line at an offset

  The elevation of a section at any offset, between its points.

  z = z₀ + (z₁ − z₀)·(o − o₀) ÷ (o₁ − o₀)

  Cross sections and end-area volumes along an alignment sections.js

  • CivilCraft
  64-bit

• Cut and fill area of a section

  The area of cut and of fill between the ground line and the design line of one section.

  per interval: area = (e₀ + e₁) ÷ 2 × w; where the lines cross: o× = o₀ + w·e₀ ÷ (e₀ − e₁), two triangles

  Cross sections and end-area volumes along an alignment sections.js

  • CivilCraft
  64-bit

• Feature line crossings

  The offset and elevation where each corridor feature line crosses the sample line.

  o = −left + (left + right)·t; z = z_p + (z_q − z_p)·u

  Cross sections and end-area volumes along an alignment sections.js

  • CivilCraft
  64-bit

• Spans inside the graded regions

  The parts of a sample line that lie inside the graded regions, which is where the design counts.

  Cross sections and end-area volumes along an alignment sections.js

  • CivilCraft
  64-bit

• Volumes between sections

  Cut and fill volume between neighboring sections and the running totals.

  V = (A₁ + A₂) ÷ 2 × (sta₂ − sta₁); cumulative = Σ V

  Cross sections and end-area volumes along an alignment sections.js

  • CivilCraft
  64-bit