Calculations

Calculations

• 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

• Overlap area of two modifiers

  The plan area where two ground-shaping objects overlap.

  overlap = |area of a| − area of (a with b cut out)

  Ground modifiers: cut and fill, overlaps, level labels and junction checks landscape/stack.js

  • CivilCraft
  64-bit

• Cut and fill per modifier

  The cut volume, fill volume and area that each ground-shaping object accounts for.

  cell = √(W × H ÷ 200000); fill += (z proposed − z existing) × cell² when positive, cut when negative

  Ground modifiers: cut and fill, overlaps, level labels and junction checks landscape/stack.js

  • CivilCraft
  64-bit

• Spot level and gradient

  The level at a point, or the fall, run, percent and ratio between two points on the surface.

  pct = |z₂ − z₁| ÷ run × 100; ratio = run ÷ |z₂ − z₁|

  Ground modifiers: cut and fill, overlaps, level labels and junction checks landscape/stack.js

  • CivilCraft
  64-bit

• Typical thresholds in project units

  The level difference that counts as meeting and the drop that counts as a trip edge.

  meet = 0.01 m × k; drop = 0.15 m × k; k = 1 ÷ 0.3048 for feet

  Ground modifiers: cut and fill, overlaps, level labels and junction checks landscape/problems-landscape.js

  • CivilCraft
  64-bit

• Paving level at a point

  The finished level of a paved area at any point: flat, on its cross-fall plane, or on its cone to a drain.

  cross: z = z₀ − (pct ÷ 100)((x − cx)·cos a + (y − cy)·sin a); drain: z = z₀ + (pct ÷ 100) × distance to the drain

  Ground modifiers: cut and fill, overlaps, level labels and junction checks landscape/problems-landscape.js

  • CivilCraft
  64-bit

• Ground against a wall's top and footing

  Finds where the ground on the high side is above the wall's top or the ground on the low side is below the footing's top.

  over = max(ground left, ground right) − top; footing shows = footing − min(ground left, ground right)

  Ground modifiers: cut and fill, overlaps, level labels and junction checks landscape/problems-landscape.js

  • CivilCraft
  64-bit

• Steps against the paving they land on

  The level difference between a flight's bottom or top and the paving at that point.

  d = z of the flight's end − paving level there

  Ground modifiers: cut and fill, overlaps, level labels and junction checks landscape/problems-landscape.js

  • CivilCraft
  64-bit

• Planted area level against a paving edge

  The largest level difference between a planted area's finished level and the paving along the edge they share.

  d = area level − paving level at the midpoint of each cut edge

  Ground modifiers: cut and fill, overlaps, level labels and junction checks landscape/problems-landscape.js

  • CivilCraft
  64-bit

• Where the section line is inside an outline

  The stretches of the section line, as distances along it, that lie inside a closed outline.

  d = distance to the segment start + t × segment length, for every crossing t

  Landscape sections and detail drawings landscape/section.js

  • CivilCraft
  64-bit

• Where the section line crosses an open line

  The distances along the section line where it crosses a wall or other open line.

  d = distance to the segment start + t × segment length

  Landscape sections and detail drawings landscape/section.js

  • CivilCraft
  64-bit

• Distance along and across the section line

  How far along the section line a point is and how far to its side, used to pick the plants drawn in the section.

  t = clamp(((p − a)·(b − a)) ÷ |b − a|², 0, 1); offset = ±|p − (a + t(b − a))|

  Landscape sections and detail drawings landscape/section.js

  • CivilCraft
  64-bit

• Proposed ground level at a distance

  The level of the proposed ground at a distance along the section, between the cut's points.

  z = z₀ + (d − d₀) ÷ (d₁ − d₀) × (z₁ − z₀)

  Landscape sections and detail drawings landscape/section.js

  • CivilCraft
  64-bit

• Build-up layers under the ground line

  Each layer of a paving or planted-area build-up drawn as a band hanging below the proposed ground.

  top of layer = ground − Σ thickness of the layers above; y = z × vertical exaggeration

  Landscape sections and detail drawings landscape/section.js

  • CivilCraft
  64-bit

• Wall at the section line

  The top and footing levels of a wall where the section line crosses it.

  values of the wall station nearest the crossing point

  Landscape sections and detail drawings landscape/section-ls.js

  • CivilCraft
  64-bit

• Steps in profile

  The stepped outline of a flight where the section line passes through it.

  risers climbed = ⌊distance along the flight ÷ going⌋ + 1; z = bottom + risers × riser

  Landscape sections and detail drawings landscape/section-ls.js

  • CivilCraft
  64-bit

• Plants near the section line

  The plants drawn in a section, with their height and spread in project units.

  h = height (m) ÷ k; k = 0.3048 for feet

  Landscape sections and detail drawings landscape/section-ls.js

  • CivilCraft
  64-bit

• Scale of a section on its sheet

  Picks the standard scale a section is drawn at and the paper millimeters per project unit.

  k = real ÷ n; real = 1000 mm per m or 304.8 mm per ft; n = first of 10, 20, 25, 50, 100, 200, 250, 500, 1000, 2000 with real ÷ n ≤ fit

  Landscape sections and detail drawings landscape/section-ls.js

  • CivilCraft
  64-bit

• Scale of a detail

  Picks the standard scale of a wall, paving or steps detail and the paper millimeters per project unit.

  k = per ÷ n; per = 1000 or 304.8; n = first of 5, 10, 20, 25, 50, 100 with 1 ÷ n ≤ fit ÷ per

  Landscape sections and detail drawings landscape/sheets.js

  • CivilCraft
  64-bit

• Wall detail: batter and footing as drawn

  The lean of the wall face and the footing shown in a wall's detail drawing.

  batter offset = tan(batter°) × (top − footing) × k; footing drawn = min(0.6 × depth, 0.3 m)

  Landscape sections and detail drawings landscape/sheets.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

• Load per meter of conductor

  The vertical load (weight and ice), the wind load and their resultant per meter of conductor in one load case.

  ice = π((D ÷ 2 + t)² − (D ÷ 2)²) × ρ × g; w_v = m·g + ice; w_h = wind pressure × (D + 2t); w = √(w_v² + w_h²)

  Overhead conductor sag and tension powerline/sag.js

  • CivilCraft
  64-bit

• Ruling span

  The equivalent span of a section between dead-ends.

  L_r = √(Σ L³ ÷ Σ L)

  Overhead conductor sag and tension powerline/sag.js

  • CivilCraft
  64-bit

• Axial stiffness and thermal expansion

  EA in newtons and the expansion coefficient per degree from the library's values.

  EA = E (GPa) × 10⁹ × area (mm²) × 10⁻⁶; α = α₆ × 10⁻⁶

  Overhead conductor sag and tension powerline/sag.js

  • CivilCraft
  64-bit

• Change of state

  The horizontal tension in a new load case and temperature, from a known tension in another.

  H³ + K·H² − M = 0; K = EA·(w₁²L² ÷ (24H₁²) + α(t₂ − t₁)) − H₁; M = EA·w₂²L² ÷ 24

  Overhead conductor sag and tension powerline/sag.js

  • CivilCraft
  64-bit

• Catenary of one span

  The lowest point, sag, conductor length and the tension at each support of a span, level or inclined.

  a = H ÷ w; x₀ = L ÷ 2 − a·asinh(dz ÷ (2a·sinh(L ÷ 2a))); y(x) = a·(cosh((x − x₀) ÷ a) − cosh(x₀ ÷ a)); length = a·(sinh((L − x₀) ÷ a) + sinh(x₀ ÷ a)); T = H·cosh(x ÷ a)

  Overhead conductor sag and tension powerline/sag.js

  • CivilCraft
  64-bit

• Horizontal tension for a support-tension limit

  The horizontal tension at which the support tension of the level ruling span equals a limit.

  find H with H·cosh(L_r·w ÷ 2H) = T

  Overhead conductor sag and tension powerline/sag.js

  • CivilCraft
  64-bit

• Meeting the tension limits on the real spans

  Lowers the reference tension until every support-tension limit holds on the actual spans, then reports which limits hold.

  H ← H ÷ max(T_max ÷ limit); holds when value ≤ limit × (1 + 1e−6)

  Overhead conductor sag and tension powerline/sag.js

  • CivilCraft
  64-bit

• Stringing table

  Tension, sag and conductor length of every span at each stringing temperature, in still air without ice.

  per temperature: change of state from the reference, then a catenary per span

  Overhead conductor sag and tension powerline/sag.js

  • CivilCraft
  64-bit

• Unbalanced ice load at a suspension support

  The longitudinal pull on a support when one adjacent span is iced and the other is bare.

  dT = max(|H iced, left − H bare, right|, |H iced, right − H bare, left|)

  Overhead conductor sag and tension powerline/sag.js

  • CivilCraft
  64-bit

• Starter library conductor data

  The area, diameter, mass, strength, stiffness, expansion and resistance of the generic stranded conductors that come with the app.

  mass = 1.02 × Σ area × density; strength = 0.9 × Σ area × wire strength; R₂₀ = 1.02 × resistivity ÷ area × 1000

  Overhead conductor sag and tension powerline/library.js

  • CivilCraft
  64-bit

• Line angle at each support

  The turn of the line at each support, in degrees.

  turn = |atan2 of the span ahead − atan2 of the span behind|, wrapped to 0 … 180°

  Overhead line checks: clearances, support loads and sizing powerline/model.js

  • CivilCraft
  64-bit

• Suspension, angle or dead-end

  Decides each support's role from the line angle when none is set.

  dead-end when turn ≥ dead-end angle; angle when turn > suspension angle

  Overhead line checks: clearances, support loads and sizing powerline/model.js

  • CivilCraft
  64-bit

• Chainage of the supports

  The cumulative horizontal distance along the line at each support, in project units.

  ch = Σ √(Δx² + Δy²)

  Overhead line checks: clearances, support loads and sizing powerline/model.js

  • CivilCraft
  64-bit

• Attachment height

  The elevation at which the conductor is attached at each support, in meters.

  attach = ground × m per unit + height above ground − fitting drop − insulator length; embedment = height ÷ 10 + 0.5 when the item gives none

  Overhead line checks: clearances, support loads and sizing powerline/checks.js

  • CivilCraft
  64-bit

• Span length and level difference

  The horizontal length of each span and the difference in attachment height between its ends.

  L = √(Δx² + Δy²) × m per unit; dz = attach right − attach left

  Overhead line checks: clearances, support loads and sizing powerline/checks.js

  • CivilCraft
  64-bit

• Clearance to the ground along a span

  The lowest height of the conductor above the ground in each load case, and where it is.

  clearance = min over samples of (attach + y(x) − ground); samples = max(20, ⌈L ÷ 2⌉) + 1

  Overhead line checks: clearances, support loads and sizing powerline/checks.js

  • CivilCraft
  64-bit

• Clearance over an obstacle

  The height of the conductor above each obstacle the span crosses in plan, in the worst load case.

  clear = min over cases of (attach + y(t × L)) − top; top = the obstacle's own top, or ground + height

  Overhead line checks: clearances, support loads and sizing powerline/checks.js

  • CivilCraft
  64-bit