Calculations

Calculations

• 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

• 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

• Meters per project unit

  The length of one project unit in meters, used by every landscape calculation that works in meters.

  1 ft = 1200 ÷ 3937 m (US survey foot); 1 m = 1

  Planting: bed and hedge fills, planted areas and their quantities landscape/planting.js

  • CivilCraft
  Exact

• Bed area

  The plan area of a bed outline.

  A = |Σ (xⱼ + xᵢ)(yⱼ − yᵢ)| ÷ 2

  Planting: bed and hedge fills, planted areas and their quantities landscape/planting.js

  • CivilCraft
  64-bit

• Whole plant counts from percentages

  Splits a number of plants among species so the counts add up to exactly that number.

  count = ⌊pct ÷ Σpct × n⌋, then the leftover goes to the largest remainders

  Planting: bed and hedge fills, planted areas and their quantities landscape/planting.js

  • CivilCraft
  64-bit

• Spacing from the plant list

  The spacing a bed or hedge is filled at when none is typed: the species' spacings weighted by their share.

  s = Σ (pct × spacing) ÷ Σ pct

  Planting: bed and hedge fills, planted areas and their quantities landscape/planting.js

  • CivilCraft
  64-bit

• Plants in a bed

  The position of every plant in a bed at the given spacing and pattern, and the count per species.

  grid step s, row pitch s (square) or s·√3 ÷ 2 (triangular); keep when inside and at least s ÷ 2 − 1e-9 from the edge

  Planting: bed and hedge fills, planted areas and their quantities landscape/planting.js

  • CivilCraft
  64-bit

• Plants along a hedge

  The number and positions of plants along a hedge line in one or two rows.

  n = ⌊length ÷ s + 1e-9⌋ + 1; first plant at (length − (n − 1)·s) ÷ 2

  Planting: bed and hedge fills, planted areas and their quantities landscape/planting.js

  • CivilCraft
  64-bit

• Offset of an open line

  A line moved sideways by a distance with mitred corners, used for hedge and path edges, obstacle footprints and IFC bodies.

  corner = p + m × d ÷ max(0.25, m·n₁), m = normalized sum of the two edge normals

  Planting: bed and hedge fills, planted areas and their quantities landscape/planting.js

  • CivilCraft
  64-bit

• Default build-up depths

  The topsoil and mulch depths a new planted area starts with, in project units.

  feet = round(meters ÷ 0.3048 × 100) ÷ 100

  Planting: bed and hedge fills, planted areas and their quantities landscape/planted.js

  • CivilCraft
  64-bit

• Plants in a clipped planted area

  The plants of a planted area after paving, walls and steps are cut out of it.

  keep when inside what is left and at least s ÷ 2 − 1e-9 from a cut edge

  Planting: bed and hedge fills, planted areas and their quantities landscape/planted.js

  • CivilCraft
  64-bit

• Planted area quantities

  The net area, perimeter, edging length, topsoil and mulch volumes and plant count of a planted area.

  topsoil = net area × topsoil depth; mulch = net area × mulch depth; edging = outline length left after clipping

  Planting: bed and hedge fills, planted areas and their quantities landscape/planted.js

  • CivilCraft
  64-bit

• Planted area quantities for takeoff

  The area, topsoil, mulch, membrane and edging quantities passed to TakeoffCraft.

  qty = round(v × 100) ÷ 100; cubic yards = cubic feet ÷ 27

  Planting: bed and hedge fills, planted areas and their quantities landscape/planted.js

  • CivilCraft
  64-bit

• Formula evaluation

  The value of a parsed formula for one row.

  + − × ÷ % ^ in 64-bit; round(x, d) = round(x × 10ᵈ) ÷ 10ᵈ

  Worksheets: formulas, column rounding and totals landscape/worksheet.js

  • CivilCraft
  64-bit

• Numbers to and from text inside a formula

  How a value is read as a number, and how a number is written when it is joined into text.

  text of a number = round(v × 10⁹) ÷ 10⁹

  Worksheets: formulas, column rounding and totals landscape/worksheet.js

  • CivilCraft
  64-bit

• Rounding a cell to its column's decimals

  Applies the column's decimals setting to a cell.

  cell = Number(v.toFixed(dec))

  Worksheets: formulas, column rounding and totals landscape/worksheet.js

  • CivilCraft
  64-bit

• Sum, count, average, minimum and maximum

  The total of a column over a group or the whole worksheet.

  sum = Σ cells; average = Σ cells ÷ n

  Worksheets: formulas, column rounding and totals landscape/worksheet.js

  • CivilCraft
  64-bit

• Rows, groups, subtotals and totals

  Builds the worksheet's rows from the objects, grouped and sorted, with subtotals and a total line.

  Worksheets: formulas, column rounding and totals landscape/worksheet.js

  • CivilCraft
  64-bit

• Route length

  The plan length of a cable route in project units.

  L = Σ √(Δx² + Δy²)

  Underground cable routes: cover, crossings, joints and trench quantities powerline/underground.js

  • CivilCraft
  64-bit

• Cover and cable band of a trench

  The cover over the cable and the thickness of the band the cable or its ducts occupy, in meters.

  cover = trench cover, or max(0, depth − bedding − band); band = duct diameter, or cable diameter

  Underground cable routes: cover, crossings, joints and trench quantities powerline/underground.js

  • CivilCraft
  64-bit

• Cable profile and cover check

  The ground and the top of the cable along the route, and whether the cover meets the minimum.

  cable = ground − cover ÷ m per unit; samples every L ÷ 100 by default

  Underground cable routes: cover, crossings, joints and trench quantities powerline/underground.js

  • CivilCraft
  64-bit

• Crossing of two plan segments

  Where two straight segments cross in plan, as a position along each.

  t = ((p − a) × e) ÷ (d × e); u = ((p − a) × d) ÷ (d × e)

  Underground cable routes: cover, crossings, joints and trench quantities powerline/underground.js

  • CivilCraft
  64-bit

• Crossings along the route

  Every place a segment crosses the route, with its chainage.

  ch = chainage of the vertex before + t × segment length

  Underground cable routes: cover, crossings, joints and trench quantities powerline/underground.js

  • CivilCraft
  64-bit

• Separation from a pipe at a crossing

  The clear vertical gap between the cable and a pipe where they cross.

  invert = (inv up + (inv down − inv up)·u) × m per unit; pipe top = invert + diameter; cable top = ground − cover; gap = max(cable bottom − pipe top, invert − cable top)

  Underground cable routes: cover, crossings, joints and trench quantities powerline/underground.js

  • CivilCraft
  64-bit

• Separation from another cable route

  The clear vertical gap between two cable routes that cross, each at its own cover under the same ground.

  gap between [−cover A − band A, −cover A] and [−cover B − band B, −cover B]

  Underground cable routes: cover, crossings, joints and trench quantities powerline/underground.js

  • CivilCraft
  64-bit

• Cables and pipes under an overhead line

  The cable routes and pipes an overhead line crosses in plan, with the line's chainage and the level of the top of each.

  cable top = ground − cover ÷ m per unit; pipe top = invert at the crossing + diameter

  Underground cable routes: cover, crossings, joints and trench quantities powerline/underground.js

  • CivilCraft
  64-bit

• Joints from the drum length

  How many joints each cable needs and where along the route they fall.

  run = length × (1 + slack %); joints per cable = ⌈run ÷ drum⌉ − 1; at = k × drum ÷ (1 + slack %)

  Underground cable routes: cover, crossings, joints and trench quantities powerline/underground.js

  • CivilCraft
  64-bit

• Trench quantities

  Trench length, excavation, bedding and backfill volumes, duct length and cable length of a route.

  excavation = width × depth × length; bedding = width × bedding × length; backfill = excavation − bedding − ducts × π(d ÷ 2)² × length; cable = (length × slack + 2 × depth) × count

  Underground cable routes: cover, crossings, joints and trench quantities powerline/underground.js

  • CivilCraft
  64-bit

• Cubic meters per cubic yard

  The factor used to give volumes in cubic yards in a feet project.

  1 yd³ = 0.764554857984 m³

  Power line tables, quantities and GIS export powerline/outputs.js

  • CivilCraft
  Exact

• Stringing table rows

  Tension, span length, sag and conductor length per section and temperature, in project units.

  length ÷ m per unit; force ÷ 10 for daN or ÷ 4.4482216152605 for lbf

  Power line tables, quantities and GIS export powerline/outputs.js

  • CivilCraft
  64-bit

• Stringing table CSV

  The stringing table as CSV text.

  lengths and sags round(v, 2); tension round(v, 1)

  Power line tables, quantities and GIS export powerline/outputs.js

  • CivilCraft
  64-bit

• Support table rows

  Ground, attachment, load, nominal load, foundation and swing per support, in project units.

  attach height = attach z − ground z; load = worst F_eq in daN or lbf

  Power line tables, quantities and GIS export powerline/outputs.js

  • CivilCraft
  64-bit

• Conductor length to buy

  The conductor length of a line with an allowance for jumpers and waste.

  length = Σ catenary lengths × phases × circuits × 1.02 ÷ m per unit

  Power line tables, quantities and GIS export powerline/outputs.js

  • CivilCraft
  64-bit

• Lengths and volumes in project units

  Converts meters and cubic meters to feet and cubic yards for the quantity rows.

  LF = m ÷ 0.3048; CY = m³ ÷ 0.764554857984

  Power line tables, quantities and GIS export powerline/outputs.js

  • CivilCraft
  64-bit