Calculations

Calculations

• 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

• Least-cost search

  Searches the grid for the cheapest allowed path and returns its points and total cost.

  grade = |z₂ − z₁| ÷ length ≤ limit; cost = length × unit cost × factor × (1 + w·(grade ÷ limit)²) + area × length × earth cost

  Best route across the terrain route.js

  • CivilCraft
  32-bit in part

• Path points and their elevations

  Turns the chain of grid cells into the route's points, with the two ends at the picked points and collinear points removed.

  x = minX + (i + 0.5) × cell; collinear when |cross product| < 1e-9 × cell²

  Best route across the terrain route.js

  • CivilCraft
  32-bit in part

• Route length, steepest grade and earthwork

  The length, steepest grade, cut and fill along a finished route.

  length = Σ √(Δx² + Δy²); grade = |Δz| ÷ l; s = |z_left − z_right| ÷ width; area = width²·s ÷ 4 ÷ max(0.05, 1 − sideSlope·s); volume += area × l ÷ n

  Best route across the terrain route.js

  • CivilCraft
  64-bit

• Curve radius at each bend

  The turn angle and the radius implied at each bend of the route.

  turn = atan2 of the leg after − atan2 of the leg before, wrapped to (−π, π]; radius = (l₁ + l₂) ÷ (2|turn|)

  Best route across the terrain route.js

  • CivilCraft
  64-bit

• Route profile

  Distance along the route against elevation, for the profile drawing and the point table.

  dᵢ = dᵢ₋₁ + √(Δx² + Δy²)

  Best route across the terrain route.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

• 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

• US gallon in cubic feet

  The factor that turns gallons into cubic feet in feet projects.

  1 gal = 0.133680556 ft³

  Sanitary sewer design flows and pipe sizes sewer.js

  • CivilCraft
  64-bit

• Peaking factor

  The ratio of peak to average sanitary flow for a population.

  Harmon: 1 + 14 ÷ (4 + √P); Babbitt: 5 ÷ P^0.2; P in thousands; held between pfMin and pfMax

  Sanitary sewer design flows and pipe sizes sewer.js

  • CivilCraft
  64-bit

• Average flow from people

  People times per-person daily flow, in project flow units.

  m: P × L/day ÷ 1000 ÷ 86400; ft: P × gal/day × 0.133680556 ÷ 86400

  Sanitary sewer design flows and pipe sizes sewer.js

  • CivilCraft
  64-bit

• Infiltration flow

  Tributary area times the infiltration allowance, in project flow units.

  m: ha × L/s per ha ÷ 1000; ft: ac × gal/day per ac × 0.133680556 ÷ 86400

  Sanitary sewer design flows and pipe sizes sewer.js

  • CivilCraft
  64-bit

• Design flow, slope and velocity per pipe

  For each pipe in flow order: the people and area above it, the peak flow, the slope, the full capacity, the normal depth and the velocity.

  S = (inv up − inv down) ÷ length; Q = q_dom × pf + q_inf; ratio = Q ÷ Q_full; V = Q ÷ A(yn)

  Sanitary sewer design flows and pipe sizes sewer.js

  • CivilCraft
  64-bit

• Pipe size for the design flow

  The smallest listed pipe size whose allowed share of full capacity carries the design flow.

  first size with Q_full(size) × maxFull ≥ Q

  Sanitary sewer design flows and pipe sizes sewer.js

  • CivilCraft
  64-bit

• Catchment runoff hydrograph

  The runoff from one catchment at each time step for a constant storm.

  q(t) = k·C·A·(depth(t) − depth(t − w)) ÷ w; depth(τ) = i·clamp(τ, 0, duration); k = 1 ÷ 360 (m), 1 (ft)

  Storm hydrographs routed through the pipe network storm-route.js

  • CivilCraft
  64-bit

• Muskingum coefficients

  The three weights of the routing equation for a reach.

  d = K(1 − X) + Δt ÷ 2; c₀ = (−KX + Δt ÷ 2) ÷ d; c₁ = (KX + Δt ÷ 2) ÷ d; c₂ = (K(1 − X) − Δt ÷ 2) ÷ d

  Storm hydrographs routed through the pipe network storm-route.js

  • CivilCraft
  64-bit

• Routing one reach

  The outflow hydrograph of a pipe from its inflow hydrograph.

  O₂ = max(0, c₀·I₂ + c₁·I₁ + c₂·O₁) on a step of max(Δt, 2KX); values between steps by linear interpolation

  Storm hydrographs routed through the pipe network storm-route.js

  • CivilCraft
  64-bit

• Travel time and weighting of each pipe

  The routing constants K and X of each pipe from its length, slope and rational peak flow.

  c = 1.5 × max(V, 0.1); K = L ÷ c ÷ 60; X = clamp(½(1 − Q ÷ (T·S·c·L)), 0, ½)

  Storm hydrographs routed through the pipe network storm-route.js

  • CivilCraft
  64-bit

• Summing flows and reading peaks

  Adds the hydrographs arriving at each structure and reads each pipe's peak in, peak out, attenuation and share of capacity.

  att = max(0, 1 − peak out ÷ peak in); ratio = peak out ÷ capacity; over when peak out > capacity × (1 + 1e-9)

  Storm hydrographs routed through the pipe network storm-route.js

  • CivilCraft
  64-bit

• Hydrograph as CSV

  Writes a structure's hydrograph as minutes and flow.

  minutes to 3 decimals; flow to 6 decimals

  Storm hydrographs routed through the pipe network storm-route.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

• Search box around a point

  The longitude and latitude box that holds a radius in meters around a point.

  Δlat = r ÷ 111320; Δlon = r ÷ (111320 × max(0.01, cos lat))

  Address to site: parcel area, distances and shares site-sources.js

  • CivilCraft
  64-bit

• Ring area

  The signed area of one polygon ring.

  A = ½ Σ (xᵢ·yᵢ₊₁ − xᵢ₊₁·yᵢ)

  Address to site: parcel area, distances and shares site-sources.js

  • CivilCraft
  64-bit