Calculations

Calculations

• 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

• Crossover between parallel tracks

  The straight between two turnouts that join parallel tracks, and the overall length.

  straight = (spacing − 2g) ÷ sin θ; length = 2 × lead + straight × cos θ

  Railway turnouts, crossovers and clearance envelopes turnout.js

  • CivilCraft
  64-bit

• Speed on the diverging route

  The speed for a radius, cant and cant deficiency.

  V = √(R·(E + D) ÷ (rail ÷ 127.12)) km/h; rail = 1500 mm gives 11.8

  Railway turnouts, crossovers and clearance envelopes turnout.js

  • CivilCraft
  64-bit

• Vehicle throw on a curve

  How far the middle of a vehicle moves in and its ends move out on a curve.

  inside = b² ÷ (8R); outside = (L² − b²) ÷ (8R)

  Railway turnouts, crossovers and clearance envelopes turnout.js

  • CivilCraft
  64-bit

• Clearance outline on a canted curve

  The vehicle or structure outline tilted by the cant and widened by the curve throw.

  tilt = asin(min(1, cant ÷ base)); rotate each point about the low rail; shift by the inside or outside throw

  Railway turnouts, crossovers and clearance envelopes turnout.js

  • CivilCraft
  64-bit

• Least track spacing for two outlines

  The smallest center spacing at which two clearance outlines do not overlap.

  bisection on the shift between 0 and 20, 60 halvings

  Railway turnouts, crossovers and clearance envelopes turnout.js

  • CivilCraft
  64-bit

• Turn angle at a junction

  The angle a main turns through at a junction of two pipes.

  turn = |atan2 of the leg after − atan2 of the leg before|, folded to 0 to 180 degrees

  Water mains as objects: depths, fittings and take-off water-objects.js

  • CivilCraft
  64-bit

• Pipe depths and derived fittings

  The elevation of each pipe end, the position of placed objects along pipes, and the fittings the layout implies.

  z = ground − cover; on a pipe: p = a + (b − a)·t; length = stated, else √(Δx² + Δy²); bend angle rounded to 0.1°

  Water mains as objects: depths, fittings and take-off water-objects.js

  • CivilCraft
  64-bit

• Take-off of pipes and fittings

  The count of each fitting by kind and size and the count and total length of pipe by size.

  length per size = Σ pipe lengths

  Water mains as objects: depths, fittings and take-off water-objects.js

  • CivilCraft
  64-bit

• Take-off as CSV

  Writes the take-off list to a CSV file.

  length = round(length × 100) ÷ 100; size to 1 decimal

  Water mains as objects: depths, fittings and take-off water-objects.js

  • CivilCraft
  64-bit

• Ground elevation of a new node

  The elevation stored on a junction, reservoir or tank when it is placed on the plan.

  z = round(ground × 100) ÷ 100; reservoir head = z + 30 (m) or 100 (ft)

  Water mains as objects: depths, fittings and take-off water-ui.js

  • CivilCraft
  64-bit

• Unit factors

  The factors that turn project units (ft, in, gpm, psi or m, mm, L/s, kPa) into the SI values the solver works in.

  ft = 0.3048 m; in = 0.0254 m; gpm = 6.30902e-5 m³/s; psi per ft = 0.433527; kPa per m = 9.80665

  Water mains network: heads, flows and pressures water.js

  • CivilCraft
  64-bit

• Pump curve fit

  Turns one or three pump curve points into the head a pump adds at any flow.

  H = H₀ − r·Qⁿ; n = ln((H₀ − H₂) ÷ (H₀ − H₁)) ÷ ln(Q₂ ÷ Q₁); r = (H₀ − H₁) ÷ Q₁ⁿ

  Water mains network: heads, flows and pressures water.js

  • CivilCraft
  64-bit

• Hazen-Williams head loss

  The friction head loss in a pipe for a given flow, length, diameter and C factor, in SI.

  h = 10.67 × L × |Q|^1.852 ÷ (C^1.852 × D^4.871) × sign(Q)

  Water mains network: heads, flows and pressures water.js

  • CivilCraft
  64-bit

• Pipe resistance and minor-loss coefficients

  The two coefficients each pipe carries into the solver: friction resistance and minor loss.

  r = 10.67 × L ÷ (C^1.852 × D^4.871); m = 8K ÷ (π² g D⁴)

  Water mains network: heads, flows and pressures water.js

  • CivilCraft
  64-bit

• Head loss and its gradient for one link

  The head loss across a pipe, valve or pump at the current flow, and its derivative, for each solver pass.

  pipe: f = (r·|q|^0.852 + m·|q|)·q, g = 1.852·r·|q|^0.852 + 2·m·|q|; pump: f = −(H₀ − r·qⁿ), g = r·n·qⁿ⁻¹

  Water mains network: heads, flows and pressures water.js

  • CivilCraft
  64-bit

• Node equations for one pass

  Builds the linear system for the unknown heads from the link coefficients, demands and fixed heads, and solves it.

  Q = P·(Hₐ − H_b) + Y; P = 1 ÷ g; Y = Q − f ÷ g; Σ flows at each node = demand

  Water mains network: heads, flows and pressures water.js

  • CivilCraft
  64-bit

• Flow update and convergence test

  Updates every link flow from the new heads and decides when the network is solved.

  stop when Σ|Q_new − Q_old| ÷ Σ|Q_new| < 1e−7 and no valve or pump changed status

  Water mains network: heads, flows and pressures water.js

  • CivilCraft
  64-bit

• Linear solve for the heads

  Solves the symmetric positive definite system for the unknown node heads.

  A = L·Lᵀ, forward and back substitution; or conjugate gradient with z = r ÷ diag(A)

  Water mains network: heads, flows and pressures water.js

  • CivilCraft
  64-bit

• Heads, pressures, velocities and head loss per 1000

  The numbers shown for each node and pipe, converted back to project units, and the limit checks on them.

  pressure = (H − z) × p factor; v = |Q| ÷ (π D² ÷ 4); loss per 1000 = |Hₐ − H_b| ÷ (L ÷ 1000)

  Water mains network: heads, flows and pressures water.js

  • CivilCraft
  64-bit

• Available fire flow

  The largest draw at one node that keeps the lowest pressure in the network at or above the residual pressure.

  bisection on the draw: 40 halvings of [lo, hi], each one a full network solve

  Water mains network: heads, flows and pressures water.js

  • CivilCraft
  64-bit

• Tank levels over time

  Steps the network through the day and moves each tank level by the flow into it.

  level₊ = level + inflow × Δt ÷ (π d² ÷ 4), clamped to [min level, max level]

  Water mains network: heads, flows and pressures water.js

  • CivilCraft
  64-bit

• EPANET-format export

  Writes the network as EPANET-format text for other programs.

  written value = round(v × 10⁴) ÷ 10⁴

  Water mains network: heads, flows and pressures water.js

  • CivilCraft
  64-bit

• Lot outline with arcs as chords

  The lot as a counter-clockwise ring of points, each tagged with the lot line it starts.

  chord angle = 2·acos(1 − 0.01 ÷ R); n = ⌈Δ ÷ chord angle⌉, 2 ≤ n ≤ 400

  Zoning envelope and limit checks zoning.js

  • CivilCraft
  64-bit

• Setback distance for each lot line

  Assigns the front, side or rear distance, or a typed distance, to every lot line, and picks the rear line when none is named.

  rear = the line with −cos(dir − front dir) > 0.5 whose midpoint is farthest from the front line's midpoint

  Zoning envelope and limit checks zoning.js

  • CivilCraft
  64-bit

• Buildable envelope and its area

  The lot taken in from every line by that line's setback, with its area, or the reason it cannot be built.

  area = |shoelace(envelope)|; lot area = |shoelace(lot ring)|

  Zoning envelope and limit checks zoning.js

  • CivilCraft
  64-bit

• Mitred inset with a distance per line

  Moves each lot line in by its own distance and finds each new corner where two moved lines meet.

  s = ((q − p) × u_q) ÷ (u_p × u_q); corner = p + s·u_p

  Zoning envelope and limit checks zoning.js

  • CivilCraft
  64-bit

• Allowed height under a sky-exposure plane

  The lowest height the cap and the sky-exposure plane allow over a footprint.

  s = ((p − a) × (b − a)) ÷ |b − a|; h = h₀ + rise × max(0, s); allowed = min over corners and lines

  Zoning envelope and limit checks zoning.js

  • CivilCraft
  64-bit

• Footprint area inside the envelope

  How much of a building footprint lies inside the buildable envelope.

  area = Σ over envelope triangles of |shoelace(footprint clipped to the triangle)|

  Zoning envelope and limit checks zoning.js

  • CivilCraft
  64-bit

• Clip a footprint to one triangle

  The part of a polygon inside a convex, counter-clockwise piece.

  side(p) = (b − a) × (p − a); crossing at u = s_p ÷ (s_p − s_q)

  Zoning envelope and limit checks zoning.js

  • CivilCraft
  64-bit

• Coverage, floor area ratio, setback and height checks

  Compares the masses on a lot with every limit typed for it and lists each result.

  coverage = Σ footprint ÷ lot area; FAR = Σ floor area ÷ lot area; outside = footprint − inside area

  Zoning envelope and limit checks zoning.js

  • CivilCraft
  64-bit

• Signed polygon area

  The signed area of a closed outline.

  A = −½ Σ (xⱼ + xᵢ)(yⱼ − yᵢ)

  Outline minus holes: area and boundary lengths landscape/areas.js

  • CivilCraft
  64-bit

• Point inside a polygon

  Whether a point lies inside an outline, used to keep or drop each boundary piece.

  count edges with (aᵧ > y) ≠ (bᵧ > y) and x < x on the edge at height y

  Outline minus holes: area and boundary lengths landscape/areas.js

  • CivilCraft
  64-bit

• Where two segments cross

  The position along one edge where another edge crosses or touches it.

  t = ((c − a) × s) ÷ (r × s); u = ((c − a) × r) ÷ (r × s)

  Outline minus holes: area and boundary lengths landscape/areas.js

  • CivilCraft
  64-bit

• Area by slabs

  The area of the outline with every hole removed, overlaps counted once.

  area = Σ over slabs of (width inside the outline and outside all holes at mid-height) × slab height

  Outline minus holes: area and boundary lengths landscape/areas.js

  • CivilCraft
  64-bit

• Outline and cut lengths

  The pieces of the outline that remain and the pieces of the holes that cut it, with their total lengths.

  length = Σ |b − a| over kept pieces; a = e.a + t₀(e.b − e.a), b = e.a + t₁(e.b − e.a)

  Outline minus holes: area and boundary lengths landscape/areas.js

  • CivilCraft
  64-bit

• Fingerprint of the source points

  A short code that changes when the source linework moves, so the linked object knows to update.

  hash of round(x × 10⁶), round(y × 10⁶) for every point

  Linework checks for linked landscape objects landscape/links.js

  • CivilCraft
  64-bit

• Clean and check a line or outline

  Drops repeated points, closes an outline and refuses linework that is too short, too far away, open or self-crossing.

  Linework checks for linked landscape objects landscape/links.js

  • CivilCraft
  64-bit

• Self-crossing test

  Whether any two edges of the line cross away from their ends.

  Linework checks for linked landscape objects landscape/links.js

  • CivilCraft
  64-bit

• STL reader

  Turns a binary or ASCII STL file into a mesh with shared vertices, scaled to millimeters.

  Freeform mesh objects: quantities and placement on the ground landscape/freeform.js

  • CivilCraft
  64-bit

• Volume, surface area, footprint and height

  The quantities of a mesh object that schedules and the IFC export report.

  V = |Σ v₀·(v₁×v₂)| ÷ 6; A = Σ |(v₁−v₀)×(v₂−v₀)| ÷ 2; height = z max − z min

  Freeform mesh objects: quantities and placement on the ground landscape/freeform.js

  • CivilCraft
  64-bit

• Convex hull of the plan points

  The outline used as the object's footprint on the plan.

  keep a turn when (a − o) × (b − o) > 0

  Freeform mesh objects: quantities and placement on the ground landscape/freeform.js

  • CivilCraft
  64-bit

• Mesh millimeters to project coordinates

  Places a mesh point on the site: scaled to project units, turned by the object's rotation and moved to its insertion point.

  x = x₀ + (x·cos a − y·sin a) × k; k = 1 ÷ (1000 × meters per project unit)

  Freeform mesh objects: quantities and placement on the ground landscape/freeform.js

  • CivilCraft
  64-bit

• Base elevation and volume below ground

  The elevation the object's base sits at, its points in project coordinates, and an estimate of how much of it is below the existing ground.

  follow: base = lowest ground sample; cut: base = typed level or mean of the samples; below ≈ Σ (ground − base) × cell²

  Freeform mesh objects: quantities and placement on the ground landscape/freeform.js

  • CivilCraft
  64-bit

• Positions and indices from an accessor

  Reads a primitive's vertex positions and triangle indices from the file's binary chunk.

  Plant 3D models for the 3D view landscape/glb.js

  • CivilCraft
  32-bit, display only