Calculations

Calculations

• Section table as CSV

  Writes station, areas, volumes and running totals to a CSV file.

  areas to 2 decimals; volumes to 1 decimal; feet projects: volume ÷ 27 (cubic yards)

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

  • CivilCraft
  64-bit

• Slope as typed

  Turns a typed slope (ratio, percent, degrees or vertical) into horizontal run per unit rise.

  percent: H = 100 ÷ p; degrees: H = 1 ÷ tan(a·π ÷ 180); ratio: H = h ÷ v

  Pad side slopes and retaining walls sides.js

  • CivilCraft
  64-bit

• Wall height at each point

  The top, bottom and height of a retaining wall at each point along the pad edge.

  h = |z_pad − z_ground|; top = max; bottom = min

  Pad side slopes and retaining walls sides.js

  • CivilCraft
  64-bit

• Wall length and face area

  The total length, face area, greatest height and average height of the walls.

  length = Σ l; face = Σ l·(h₁ + h₂) ÷ 2; average height = face ÷ length

  Pad side slopes and retaining walls sides.js

  • CivilCraft
  64-bit

• Tall wall and steep slope checks

  Flags a wall higher than the limit and a cut or fill slope steeper than the limit.

  wall: h > limit + 1e-9; slope: H < max slope − 1e-9

  Pad side slopes and retaining walls sides.js

  • CivilCraft
  64-bit

• Major contour test

  Decides whether a contour goes on the major layer and gets an elevation label.

  major when |z ÷ M − round(z ÷ M)| < 1e-6, M = interval × major count

  Plan drawing and section sheets for DXF and PDF scene.js

  • CivilCraft
  64-bit

• Alignment curves as arcs

  Writes each curve of an alignment as an arc with its center, radius and start and end angles.

  a₁ = a₀ ± Δ; arc from a₀ to a₁ counterclockwise

  Plan drawing and section sheets for DXF and PDF scene.js

  • CivilCraft
  64-bit

• Pipe line between structure walls

  Draws each pipe from the wall of one structure to the wall of the next.

  round: half = outside width ÷ 2; rectangle: half = min(L ÷ 2 ÷ |u·along|, W ÷ 2 ÷ |u·across|)

  Plan drawing and section sheets for DXF and PDF scene.js

  • CivilCraft
  64-bit

• Scene to DXF entities

  Turns the scene's lines, arcs, points and labels into the entities the DXF writer takes.

  text height = paper mm ÷ (mm per model unit); middle-anchored text moved by height ÷ 2 across its direction

  Plan drawing and section sheets for DXF and PDF scene.js

  • CivilCraft
  64-bit

• Section cell size and vertical exaggeration

  Sizes the cell every section is drawn in and picks the largest vertical exaggeration that fits the page.

  width = (left + right)·s + margins; height = 1.2 × largest relief × s × vex + margins; vex = the largest of 10, 5, 2, 1 not above the wanted one that fits

  Plan drawing and section sheets for DXF and PDF section-sheets.js

  • CivilCraft
  64-bit

• Vertical scale label

  The vertical scale printed in the title strip of a section sheet.

  m: 1 : round(1000 ÷ sv); ft: 1 inch = (25.4 ÷ sv) feet, to 1 decimal

  Plan drawing and section sheets for DXF and PDF section-sheets.js

  • CivilCraft
  64-bit

• Section points on paper

  Places each section's ground and design points, grid lines and labels in its cell.

  X = x₀ + (o + left)·s; Y = y₀ + (z − z₀)·sv; z₀ = floor((z_mid − span ÷ 2) ÷ step)·step

  Plan drawing and section sheets for DXF and PDF section-sheets.js

  • CivilCraft
  64-bit

• Meters per unit for units found in files

  The factor for each linear unit name a LandXML file can carry.

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

  Typed lengths, stations and unit text units.js

  • CivilCraft
  Exact

• One typed length

  Reads one length as typed (plain number, feet and inches, fraction, mm, cm or m) into project units.

  feet + inches ÷ 12; meter project: feet × 12 × 0.0254; feet project, metric mark: meters ÷ 0.0254 ÷ 12

  Typed lengths, stations and unit text units.js

  • CivilCraft
  64-bit

• Station text

  Writes a station as text, such as 12+34.56 in feet or 1+234.567 in meters.

  r = round(|sta|, decimals); whole = floor(r ÷ station length + 1e-9); rest = r − whole × station length

  Typed lengths, stations and unit text units.js

  • CivilCraft
  64-bit

• Station as typed

  Reads a station typed as 12+34.56 or as a plain number.

  value = whole × station length + rest

  Typed lengths, stations and unit text units.js

  • CivilCraft
  64-bit

• Volume text

  Writes a volume in cubic yards or cubic meters, or in the volume unit chosen in Settings.

  feet: V ÷ 27 cu yd; chosen unit: V × (m per unit)³ through the shared unit table

  Typed lengths, stations and unit text units.js

  • CivilCraft
  64-bit

• Area text

  Writes an area in square feet or square meters, or in the area unit chosen in Settings.

  chosen unit: A × (m per unit)² through the shared unit table

  Typed lengths, stations and unit text units.js

  • CivilCraft
  64-bit

• Bearing text

  Writes a direction as a quadrant bearing in degrees, minutes and seconds.

  azimuth = (90 − a·180 ÷ π) mod 360; quadrant angle to whole seconds

  Typed lengths, stations and unit text units.js

  • CivilCraft
  64-bit

• Degrees, minutes, seconds

  Splits an angle in degrees into whole degrees, minutes and seconds.

  s = round(|deg| × 3600); d = floor(s ÷ 3600); m = floor(rest ÷ 60)

  Typed lengths, stations and unit text units.js

  • CivilCraft
  64-bit

• Turn angle at a point

  The signed turn of the line at a point of intersection.

  Δ = atan2 of the leg after − atan2 of the leg before, wrapped to (−π, π]

  Why a curve does not fit, and the radius or length that would solve-why.js

  • CivilCraft
  64-bit

• Tangent length of each curve

  The turn and the tangent length each curve takes on either side of its point.

  T = r × tan(|Δ| ÷ 2)

  Why a curve does not fit, and the radius or length that would solve-why.js

  • CivilCraft
  64-bit

• Largest radius that fits

  The largest radius at a point that fits between its neighbors' curves as they are.

  room = min(d_before − T_before, d_after − T_after); r_max = room ÷ tan(|Δ| ÷ 2)

  Why a curve does not fit, and the radius or length that would solve-why.js

  • CivilCraft
  64-bit

• Overlapping curves and the fixes offered

  Finds neighboring curves whose tangents overlap and offers radii that fit.

  overlap when Tₐ + T_b > L + 1e-9; both scaled by f = L ÷ (Tₐ + T_b); offered radius = floor(r × 100 + 1e-9) ÷ 100

  Why a curve does not fit, and the radius or length that would solve-why.js

  • CivilCraft
  64-bit

• Vertical curves that do not fit

  Finds vertical curves longer than the room between their neighbors and offers the longest length that fits.

  A = (g₂ − g₁) × 100; L = K × |A| when given by K; room = 2 × min(back, forward); offered L = floor(room × 100 + 1e-9) ÷ 100; K = L ÷ |A|

  Why a curve does not fit, and the radius or length that would solve-why.js

  • CivilCraft
  64-bit

• Stations to stake

  Every multiple of the step between two stations, both ends, and the alignment's own curve points in between.

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

  Staking reports staking.js

  • CivilCraft
  64-bit

• Stake position

  The coordinates of a stake at a station and an offset to the right or left.

  x = xₚ + off × sin(dir); y = yₚ − off × cos(dir)

  Staking reports staking.js

  • CivilCraft
  64-bit

• Stake rows with cut or fill

  One row per station and offset with design elevation, ground elevation and cut or fill.

  cf = ground − design (positive = cut)

  Staking reports staking.js

  • CivilCraft
  64-bit

• Survey points against the alignment

  Each survey point's station and offset on the alignment, the design there and the cut or fill to the point's own elevation.

  cf = point elevation − design

  Staking reports staking.js

  • CivilCraft
  64-bit

• Staking table as CSV

  Writes the stake rows to a CSV file.

  northing, easting, design, ground and cut or fill to 3 decimals; offset and the C/F column to 2 decimals

  Staking reports staking.js

  • CivilCraft
  64-bit

• Millimeters per project unit

  The factor from project feet or meters to millimeters.

  m: 1000; ft: 1,200,000 ÷ 3937 (US survey foot)

  Drainage structure types and their library items structs.js

  • CivilCraft
  Exact

• Inside and outside size of a structure

  The inside and outside width and length, the wall and the frame of a structure in project units.

  inside = size ÷ P; outside = inside + 2 × wall ÷ P; P = 12 (inches per foot) or 1000 (mm per m)

  Drainage structure types and their library items structs.js

  • CivilCraft
  64-bit

• Plan shapes of a type

  The outside wall, inside wall and frame opening of a type as plan shapes in millimeters.

  r = round₆((size × M) ÷ 2); M = 25.4 (inch) or 1 (mm)

  Drainage structure types and their library items structs.js

  • CivilCraft
  64-bit

• Round outline as a polygon

  The outline of a round structure's body as points on a circle.

  pᵢ = (r·cos(2π·i ÷ n), r·sin(2π·i ÷ n)), n = 48

  Drainage structure types and their library items structs.js

  • CivilCraft
  64-bit

• Library item of a type

  The library item for a type: its body from the underside of the floor slab to the rim, its sizes, and every parameter in millimeters.

  H = depth × U + base × M; body = outline from −H to 0; parameters as text of (value × factor)

  Drainage structure types and their library items structs.js

  • CivilCraft
  64-bit

• Type read back from a library item

  Turns a library item's millimeter parameters back into a type in the project's units.

  value = millimeters ÷ M (sizes) or ÷ U (sump, depth)

  Drainage structure types and their library items structs.js

  • CivilCraft
  64-bit

• Length of a polyline

  The plan length of a polyline.

  L = Σ √(Δx² + Δy²)

  Section cut from the ground along any line terrain-section.js

  • CivilCraft
  64-bit

• Point at a distance along a line

  The point and direction at a distance along a polyline.

  u = (d − length before the segment) ÷ segment length, clamped to [0, 1]; p = a + (b − a)·u

  Section cut from the ground along any line terrain-section.js

  • CivilCraft
  64-bit

• Nearest point on a line

  The distance along a polyline and the offset to the side of the point nearest to a given point.

  u = ((p − a)·(b − a)) ÷ |b − a|², clamped; d = length before + u·|b − a|; offset = ± distance, sign from the cross product

  Section cut from the ground along any line terrain-section.js

  • CivilCraft
  64-bit

• Crossing of two segments

  Where two segments cross, as fractions along each.

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

  Section cut from the ground along any line terrain-section.js

  • CivilCraft
  64-bit

• First crossing of two polylines

  The first place one polyline crosses another, with the distance along each.

  d_a = length before + t·|segment a|; d_b = length before + u·|segment b|

  Section cut from the ground along any line terrain-section.js

  • CivilCraft
  64-bit

• Line square to a polyline

  A straight line square to a polyline at a distance along it, a set length to each side.

  right = (sin dir, −cos dir); p = c − right × left; q = c + right × right length

  Section cut from the ground along any line terrain-section.js

  • CivilCraft
  64-bit

• Section along a line

  The points of the ground along a line: distance, offset, coordinates and elevation at every triangle edge crossing and line vertex.

  d = length before + t·|segment|; o = d − origin; z from the surface at (x, y)

  Section cut from the ground along any line terrain-section.js

  • CivilCraft
  64-bit

• Elevation of a section at an offset

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

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

  Section cut from the ground along any line terrain-section.js

  • CivilCraft
  64-bit

• Angular misclosure and leg directions

  The angular misclosure of a loop and the direction of each leg after the angles are corrected.

  misclosure = ((again − first) mod 360 + 540) mod 360 − 180; per angle = −misclosure ÷ n; az(i) = az(i − 1) + 180 + angle(i) + per angle

  Traverse closure and compass adjustment traverse.js

  • CivilCraft
  64-bit

• Station coordinates and linear misclosure

  The unadjusted coordinates of each station, the misclosure at the end and the traverse's precision.

  x += d·cos(dir); y += d·sin(dir); misclosure = √(Δx² + Δy²); precision = total length ÷ misclosure

  Traverse closure and compass adjustment traverse.js

  • CivilCraft
  64-bit

• Compass rule adjustment

  Moves each station against the misclosure in proportion to the distance run to reach it.

  cx = −Δx × run ÷ length; cy = −Δy × run ÷ length; adjusted = unadjusted + correction

  Traverse closure and compass adjustment traverse.js

  • CivilCraft
  64-bit

• Traverse report as CSV

  Writes the closure and every station's unadjusted and adjusted coordinates and corrections.

  coordinates and corrections to 4 decimals; distances and length to 3; precision as 1 : whole number; angles to whole seconds

  Traverse closure and compass adjustment traverse.js

  • CivilCraft
  64-bit

• Frog angle from the frog number

  The angle at which the diverging track leaves, from the frog number.

  θ = 2·atan(1 ÷ (2N))

  Railway turnouts, crossovers and clearance envelopes turnout.js

  • CivilCraft
  64-bit

• Turnout radius, lead and centerline

  The closure radius, the lead and the centerline points of the diverging track.

  R = (g − s·sin β) ÷ (cos β − cos θ); lead = s·cos β + R·(sin θ − sin β); arc length = R·(θ − β)

  Railway turnouts, crossovers and clearance envelopes turnout.js

  • CivilCraft
  64-bit